diff --git a/Library/Homebrew/bundle/cask_dumper.rb b/Library/Homebrew/bundle/cask_dumper.rb
index b3381d1ae8..ef1059b7e4 100644
--- a/Library/Homebrew/bundle/cask_dumper.rb
+++ b/Library/Homebrew/bundle/cask_dumper.rb
@@ -8,6 +8,7 @@ module Homebrew
         @casks = nil
         @cask_names = nil
         @cask_hash = nil
+        @cask_oldnames = nil
       end
 
       def self.cask_names
@@ -38,6 +39,25 @@ module Homebrew
         end.join("\n")
       end
 
+      def self.cask_oldnames
+        return @cask_oldnames if @cask_oldnames
+
+        @cask_oldnames = {}
+        casks.each do |c|
+          oldnames = c.old_tokens
+          next if oldnames.blank?
+
+          oldnames.each do |oldname|
+            @cask_oldnames[oldname] = c.full_name
+            if c.full_name.include? "/" # tap cask
+              tap_name = c.full_name.rpartition("/").first
+              @cask_oldnames["#{tap_name}/#{oldname}"] = c.full_name
+            end
+          end
+        end
+        @cask_oldnames
+      end
+
       def self.formula_dependencies(cask_list)
         return [] unless Bundle.cask_installed?
         return [] if cask_list.blank?
diff --git a/Library/Homebrew/bundle/cask_installer.rb b/Library/Homebrew/bundle/cask_installer.rb
index 4014666d73..c559fa8523 100644
--- a/Library/Homebrew/bundle/cask_installer.rb
+++ b/Library/Homebrew/bundle/cask_installer.rb
@@ -87,12 +87,25 @@ module Homebrew
         !cask_upgradable?(cask)
       end
 
+      def self.cask_in_array?(cask, array)
+        return true if array.include?(cask)
+        return true if array.include?(cask.split("/").last)
+
+        require "bundle/cask_dumper"
+        old_names = Homebrew::Bundle::CaskDumper.cask_oldnames
+        old_name = old_names[cask]
+        old_name ||= old_names[cask.split("/").last]
+        return true if old_name && array.include?(old_name)
+
+        false
+      end
+
       def self.cask_installed?(cask)
-        installed_casks.include? cask
+        cask_in_array?(cask, installed_casks)
       end
 
       def self.cask_upgradable?(cask)
-        outdated_casks.include? cask
+        cask_in_array?(cask, outdated_casks)
       end
 
       def self.installed_casks
diff --git a/Library/Homebrew/bundle/commands/cleanup.rb b/Library/Homebrew/bundle/commands/cleanup.rb
index f72aaee03c..20f99f9208 100644
--- a/Library/Homebrew/bundle/commands/cleanup.rb
+++ b/Library/Homebrew/bundle/commands/cleanup.rb
@@ -128,9 +128,10 @@ module Homebrew
             kept_formulae = @dsl.entries.select { |e| e.type == :brew }.map(&:name)
             kept_formulae += Homebrew::Bundle::CaskDumper.formula_dependencies(kept_casks)
             kept_formulae.map! do |f|
-              Homebrew::Bundle::FormulaDumper.formula_aliases[f] ||
-                Homebrew::Bundle::FormulaDumper.formula_oldnames[f] ||
-                f
+              Homebrew::Bundle::FormulaDumper.formula_aliases.fetch(
+                f,
+                Homebrew::Bundle::FormulaDumper.formula_oldnames.fetch(f, f),
+              )
             end
 
             kept_formulae + recursive_dependencies(Homebrew::Bundle::FormulaDumper.formulae, kept_formulae)
@@ -142,7 +143,11 @@ module Homebrew
           return @kept_casks if @kept_casks
 
           @dsl ||= Brewfile.read(global:, file:)
-          @kept_casks = @dsl.entries.select { |e| e.type == :cask }.map(&:name)
+          kept_casks = @dsl.entries.select { |e| e.type == :cask }.flat_map(&:name)
+          kept_casks.map! do |c|
+            Homebrew::Bundle::CaskDumper.cask_oldnames.fetch(c, c)
+          end
+          @kept_casks = kept_casks
         end
 
         private_class_method def self.recursive_dependencies(current_formulae, formulae_names, top_level: true)
diff --git a/Library/Homebrew/test/bundle/cask_dumper_spec.rb b/Library/Homebrew/test/bundle/cask_dumper_spec.rb
index 857176b1d5..c9518ee92c 100644
--- a/Library/Homebrew/test/bundle/cask_dumper_spec.rb
+++ b/Library/Homebrew/test/bundle/cask_dumper_spec.rb
@@ -95,6 +95,27 @@ RSpec.describe Homebrew::Bundle::CaskDumper do
     end
   end
 
+  describe "#cask_oldnames" do
+    before do
+      described_class.reset!
+    end
+
+    it "returns an empty string when no casks are installed" do
+      expect(dumper.cask_oldnames).to eql({})
+    end
+
+    it "returns a hash with installed casks old names" do
+      foo = instance_double(Cask::Cask, to_s: "foo", old_tokens: ["oldfoo"], full_name: "qux/quuz/foo")
+      bar = instance_double(Cask::Cask, to_s: "bar", old_tokens: [], full_name: "bar")
+      allow(Cask::Caskroom).to receive(:casks).and_return([foo, bar])
+      allow(Homebrew::Bundle).to receive(:cask_installed?).and_return(true)
+      expect(dumper.cask_oldnames).to eql({
+        "qux/quuz/oldfoo" => "qux/quuz/foo",
+        "oldfoo"          => "qux/quuz/foo",
+      })
+    end
+  end
+
   describe "#formula_dependencies" do
     context "when the given casks don't have formula dependencies" do
       before do
diff --git a/Library/Homebrew/test/bundle/commands/cleanup_spec.rb b/Library/Homebrew/test/bundle/commands/cleanup_spec.rb
index 506817cc7c..efecab654f 100644
--- a/Library/Homebrew/test/bundle/commands/cleanup_spec.rb
+++ b/Library/Homebrew/test/bundle/commands/cleanup_spec.rb
@@ -38,7 +38,9 @@ RSpec.describe Homebrew::Bundle::Commands::Cleanup do
     end
 
     it "computes which casks to uninstall" do
-      allow(Homebrew::Bundle::CaskDumper).to receive(:casks).and_return(%w[123 456])
+      cask_123 = instance_double(Cask::Cask, to_s: "123", old_tokens: [])
+      cask_456 = instance_double(Cask::Cask, to_s: "456", old_tokens: [])
+      allow(Homebrew::Bundle::CaskDumper).to receive(:casks).and_return([cask_123, cask_456])
       expect(described_class.casks_to_uninstall).to eql(%w[456])
     end