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/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/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)