diff --git a/Library/Homebrew/cask/cask.rb b/Library/Homebrew/cask/cask.rb
index 18549c48a0..1a9b2d1bde 100644
--- a/Library/Homebrew/cask/cask.rb
+++ b/Library/Homebrew/cask/cask.rb
@@ -85,9 +85,9 @@ module Cask
     # An old name for the cask.
     sig { returns(T::Array[String]) }
     def old_tokens
-      @old_tokens ||= if tap
-        tap.cask_renames
-           .flat_map { |old_token, new_token| (new_token == token) ? old_token : [] }
+      @old_tokens ||= if (tap = self.tap)
+        Tap.reverse_tap_migrations_renames.fetch("#{tap}/#{token}", []) +
+          tap.reverse_cask_renames.fetch(token, [])
       else
         []
       end
diff --git a/Library/Homebrew/cask/cask_loader.rb b/Library/Homebrew/cask/cask_loader.rb
index 76eae2ee52..1a3cd08ec3 100644
--- a/Library/Homebrew/cask/cask_loader.rb
+++ b/Library/Homebrew/cask/cask_loader.rb
@@ -522,23 +522,23 @@ module Cask
       type = nil
 
       if (new_token = tap.cask_renames[token].presence)
-        old_token = token
+        old_token = tap.core_cask_tap? ? token : tapped_token
         token = new_token
         new_token = tap.core_cask_tap? ? token : "#{tap}/#{token}"
         type = :rename
       elsif (new_tap_name = tap.tap_migrations[token].presence)
-        new_tap_user, new_tap_repo, = new_tap_name.split("/")
-        new_tap_name = "#{new_tap_user}/#{new_tap_repo}"
-        new_tap = Tap.fetch(new_tap_name)
+        new_tap_user, new_tap_repo, new_token = new_tap_name.split("/", 3)
+        new_token ||= token
+        new_tap = Tap.fetch(new_tap_user, new_tap_repo)
         new_tap.ensure_installed!
-        new_tapped_token = "#{new_tap_name}/#{token}"
+        new_tapped_token = "#{new_tap}/#{new_token}"
 
         if tapped_token == new_tapped_token
           opoo "Tap migration for #{tapped_token} points to itself, stopping recursion."
         else
+          old_token = tap.core_cask_tap? ? token : tapped_token
           token, tap, = tap_cask_token_type(new_tapped_token, warn: false)
-          old_token = tapped_token
-          new_token = new_tap.core_cask_tap? ? token : new_tapped_token
+          new_token = new_tap.core_cask_tap? ? token : "#{tap}/#{token}"
           type = :migration
         end
       end
diff --git a/Library/Homebrew/cask/caskroom.rb b/Library/Homebrew/cask/caskroom.rb
index 272685dc59..43abdfcd1f 100644
--- a/Library/Homebrew/cask/caskroom.rb
+++ b/Library/Homebrew/cask/caskroom.rb
@@ -53,7 +53,7 @@ module Cask
     sig { params(config: T.nilable(Config)).returns(T::Array[Cask]) }
     def self.casks(config: nil)
       tokens.sort.map do |token|
-        CaskLoader.load(token, config: config)
+        CaskLoader.load(token, config: config, warn: false)
       rescue TapCaskAmbiguityError
         tap_path = CaskLoader.tap_paths(token).first
         CaskLoader::FromPathLoader.new(tap_path).load(config: config)
diff --git a/Library/Homebrew/caveats.rb b/Library/Homebrew/caveats.rb
index dcf8e7a18a..1a7469e8c8 100644
--- a/Library/Homebrew/caveats.rb
+++ b/Library/Homebrew/caveats.rb
@@ -129,16 +129,16 @@ class Caveats
         Bash completion has been installed to:
           #{root_dir}/etc/bash_completion.d
       EOS
-    when :zsh
-      <<~EOS
-        zsh #{installed.join(" and ")} have been installed to:
-          #{root_dir}/share/zsh/site-functions
-      EOS
     when :fish
       fish_caveats = +"fish #{installed.join(" and ")} have been installed to:"
       fish_caveats << "\n  #{root_dir}/share/fish/vendor_completions.d" if completion_installed
       fish_caveats << "\n  #{root_dir}/share/fish/vendor_functions.d" if functions_installed
       fish_caveats.freeze
+    when :zsh
+      <<~EOS
+        zsh #{installed.join(" and ")} have been installed to:
+          #{root_dir}/share/zsh/site-functions
+      EOS
     end
   end
 
diff --git a/Library/Homebrew/formula.rb b/Library/Homebrew/formula.rb
index 3cce9ccb3f..f5a60ca97f 100644
--- a/Library/Homebrew/formula.rb
+++ b/Library/Homebrew/formula.rb
@@ -540,7 +540,12 @@ class Formula
   # Old names for the formula.
   sig { returns(T::Array[String]) }
   def oldnames
-    @oldnames ||= tap&.formula_oldnames&.dig(name) || []
+    @oldnames ||= if (tap = self.tap)
+      Tap.reverse_tap_migrations_renames.fetch("#{tap}/#{name}", []) +
+        tap.formula_reverse_renames.fetch(name, [])
+    else
+      []
+    end
   end
 
   # All aliases for the formula.
diff --git a/Library/Homebrew/formulary.rb b/Library/Homebrew/formulary.rb
index 13dccfb851..74ba8e75a4 100644
--- a/Library/Homebrew/formulary.rb
+++ b/Library/Homebrew/formulary.rb
@@ -904,7 +904,7 @@ module Formulary
 
   def self.tap_formula_name_type(tapped_name, warn:)
     user, repo, name = tapped_name.split("/", 3).map(&:downcase)
-    tap = Tap.fetch user, repo
+    tap = Tap.fetch(user, repo)
     type = nil
     alias_name = tap.core_tap? ? name : "#{tap}/#{name}"
 
@@ -912,23 +912,23 @@ module Formulary
       name = possible_alias.split("/").last
       type = :alias
     elsif (new_name = tap.formula_renames[name].presence)
-      old_name = name
+      old_name = tap.core_tap? ? name : tapped_name
       name = new_name
       new_name = tap.core_tap? ? name : "#{tap}/#{name}"
       type = :rename
     elsif (new_tap_name = tap.tap_migrations[name].presence)
-      new_tap_user, new_tap_repo, = new_tap_name.split("/")
-      new_tap_name = "#{new_tap_user}/#{new_tap_repo}"
-      new_tap = Tap.fetch new_tap_name
+      new_tap_user, new_tap_repo, new_name = new_tap_name.split("/", 3)
+      new_name ||= name
+      new_tap = Tap.fetch(new_tap_user, new_tap_repo)
       new_tap.ensure_installed!
-      new_tapped_name = "#{new_tap_name}/#{name}"
+      new_tapped_name = "#{new_tap}/#{new_name}"
 
       if tapped_name == new_tapped_name
         opoo "Tap migration for #{tapped_name} points to itself, stopping recursion."
       else
+        old_name = tap.core_tap? ? name : tapped_name
         name, tap, = tap_formula_name_type(new_tapped_name, warn: false)
-        old_name = tapped_name
-        new_name = new_tap.core_tap? ? name : new_tapped_name
+        new_name = new_tap.core_tap? ? name : "#{tap}/#{name}"
         type = :migration
       end
     end
diff --git a/Library/Homebrew/keg.rb b/Library/Homebrew/keg.rb
index 5a5453bac8..5b5d25e8fc 100644
--- a/Library/Homebrew/keg.rb
+++ b/Library/Homebrew/keg.rb
@@ -335,10 +335,10 @@ class Keg
   def completion_installed?(shell)
     dir = case shell
     when :bash then path/"etc/bash_completion.d"
+    when :fish then path/"share/fish/vendor_completions.d"
     when :zsh
       dir = path/"share/zsh/site-functions"
       dir if dir.directory? && dir.children.any? { |f| f.basename.to_s.start_with?("_") }
-    when :fish then path/"share/fish/vendor_completions.d"
     end
     dir&.directory? && !dir.children.empty?
   end
diff --git a/Library/Homebrew/tap.rb b/Library/Homebrew/tap.rb
index 962b3566ab..f3d86c3649 100644
--- a/Library/Homebrew/tap.rb
+++ b/Library/Homebrew/tap.rb
@@ -758,6 +758,15 @@ class Tap
     end
   end
 
+  # Hash with tap formula old names. Reverse of {#formula_renames}.
+  sig { returns(T::Hash[String, T::Array[String]]) }
+  def reverse_cask_renames
+    @reverse_cask_renames ||= cask_renames.each_with_object({}) do |(old_name, new_name), hash|
+      hash[new_name] ||= []
+      hash[new_name] << old_name
+    end
+  end
+
   # Hash with tap formula renames.
   sig { returns(T::Hash[String, String]) }
   def formula_renames
@@ -770,15 +779,30 @@ class Tap
 
   # Hash with tap formula old names. Reverse of {#formula_renames}.
   sig { returns(T::Hash[String, T::Array[String]]) }
-  def formula_oldnames
-    @formula_oldnames ||= formula_renames.each_with_object({}) do |(old_name, new_name), hash|
+  def formula_reverse_renames
+    @formula_reverse_renames ||= formula_renames.each_with_object({}) do |(old_name, new_name), hash|
       hash[new_name] ||= []
       hash[new_name] << old_name
     end
   end
 
+  sig { returns(T::Hash[String, T::Array[String]]) }
+  def self.reverse_tap_migrations_renames
+    Tap.each_with_object({}) do |tap, hash|
+      tap.tap_migrations.each do |old_name, new_name|
+        new_tap_user, new_tap_repo, new_name = new_name.split("/", 3)
+        next unless new_name
+
+        new_tap = Tap.fetch(new_tap_user, new_tap_repo)
+
+        hash["#{new_tap}/#{new_name}"] ||= []
+        hash["#{new_tap}/#{new_name}"] << old_name
+      end
+    end
+  end
+
   # Hash with tap migrations.
-  sig { returns(Hash) }
+  sig { returns(T::Hash[String, String]) }
   def tap_migrations
     @tap_migrations ||= if (migration_file = path/HOMEBREW_TAP_MIGRATIONS_FILE).file?
       JSON.parse(migration_file.read)
diff --git a/Library/Homebrew/test/caveats_spec.rb b/Library/Homebrew/test/caveats_spec.rb
index ad493a6c37..3a8ce307db 100644
--- a/Library/Homebrew/test/caveats_spec.rb
+++ b/Library/Homebrew/test/caveats_spec.rb
@@ -301,28 +301,34 @@ describe Caveats do
       let(:caveats) { described_class.new(f).caveats }
       let(:path) { f.prefix.resolved_path }
 
+      let(:bash_completion_dir) { path/"etc/bash_completion.d" }
+      let(:fish_vendor_completions) { path/"share/fish/vendor_completions.d" }
+      let(:zsh_site_functions) { path/"share/zsh/site-functions" }
+
       before do
         # don't try to load/fetch gcc/glibc
         allow(DevelopmentTools).to receive_messages(needs_libc_formula?: false, needs_compiler_formula?: false)
 
-        allow_any_instance_of(Pathname).to receive(:children).and_return([Pathname.new("child")])
         allow_any_instance_of(Object).to receive(:which).with(any_args).and_return(Pathname.new("shell"))
         allow(Utils::Shell).to receive_messages(preferred: nil, parent: nil)
       end
 
-      it "gives dir where Bash completions have been installed" do
-        (path/"etc/bash_completion.d").mkpath
+      it "includes where Bash completions have been installed to" do
+        bash_completion_dir.mkpath
+        FileUtils.touch bash_completion_dir/f.name
         expect(caveats).to include(HOMEBREW_PREFIX/"etc/bash_completion.d")
       end
 
-      it "gives dir where zsh completions have been installed" do
-        (path/"share/zsh/site-functions").mkpath
-        expect(caveats).to include(HOMEBREW_PREFIX/"share/zsh/site-functions")
+      it "includes where fish completions have been installed to" do
+        fish_vendor_completions.mkpath
+        FileUtils.touch fish_vendor_completions/f.name
+        expect(caveats).to include(HOMEBREW_PREFIX/"share/fish/vendor_completions.d")
       end
 
-      it "gives dir where fish completions have been installed" do
-        (path/"share/fish/vendor_completions.d").mkpath
-        expect(caveats).to include(HOMEBREW_PREFIX/"share/fish/vendor_completions.d")
+      it "includes where zsh completions have been installed to" do
+        zsh_site_functions.mkpath
+        FileUtils.touch zsh_site_functions/f.name
+        expect(caveats).to include(HOMEBREW_PREFIX/"share/zsh/site-functions")
       end
     end
   end
diff --git a/Library/Homebrew/test/support/helper/cask.rb b/Library/Homebrew/test/support/helper/cask.rb
index 8f14f52649..fa5ee7a65b 100644
--- a/Library/Homebrew/test/support/helper/cask.rb
+++ b/Library/Homebrew/test/support/helper/cask.rb
@@ -8,8 +8,8 @@ module Test
       def stub_cask_loader(cask, ref = cask.token, call_original: false)
         allow(::Cask::CaskLoader).to receive(:for).and_call_original if call_original
 
-        loader = ::Cask::CaskLoader::FromInstanceLoader.new cask
-        allow(::Cask::CaskLoader).to receive(:for).with(ref, warn: true).and_return(loader)
+        loader = ::Cask::CaskLoader::FromInstanceLoader.new(cask)
+        allow(::Cask::CaskLoader).to receive(:for).with(ref, any_args).and_return(loader)
       end
     end
   end