diff --git a/Library/Homebrew/cask/cask_loader.rb b/Library/Homebrew/cask/cask_loader.rb
index f64a5c70ae24a..361520c73bfd7 100644
--- a/Library/Homebrew/cask/cask_loader.rb
+++ b/Library/Homebrew/cask/cask_loader.rb
@@ -715,7 +715,12 @@ def self.tap_cask_token_type(tapped_token, warn:)
         end
       end
 
-      opoo "Cask #{old_token} was renamed to #{new_token}." if warn && old_token && new_token
+      if warn && old_token && new_token
+        destination_exists = find_cask_in_tap(token, tap).exist? ||
+                             (tap.core_cask_tap? && !Homebrew::EnvConfig.no_install_from_api? &&
+                              Homebrew::API.cask_tokens.include?(token))
+        opoo "Cask #{old_token} was renamed to #{new_token}." if destination_exists
+      end
 
       [token, tap, type]
     end
diff --git a/Library/Homebrew/formulary.rb b/Library/Homebrew/formulary.rb
index 6c5e1128f6c3e..b51b5f11b0ea2 100644
--- a/Library/Homebrew/formulary.rb
+++ b/Library/Homebrew/formulary.rb
@@ -1190,7 +1190,12 @@ def self.tap_formula_name_type(tapped_name, warn:)
       end
     end
 
-    opoo "Formula #{old_name} was renamed to #{new_name}." if warn && old_name && new_name
+    if warn && old_name && new_name
+      destination_exists = find_formula_in_tap(name, tap).exist? ||
+                           (tap.core_tap? && !Homebrew::EnvConfig.no_install_from_api? &&
+                            Homebrew::API.formula_names.include?(name))
+      opoo "Formula #{old_name} was renamed to #{new_name}." if destination_exists
+    end
 
     [name, tap, type]
   end
diff --git a/Library/Homebrew/test/cask/cask_loader_spec.rb b/Library/Homebrew/test/cask/cask_loader_spec.rb
index 4bd2bd601599f..ee95caa4ca95f 100644
--- a/Library/Homebrew/test/cask/cask_loader_spec.rb
+++ b/Library/Homebrew/test/cask/cask_loader_spec.rb
@@ -81,7 +81,7 @@
           (old_tap.path/"tap_migrations.json").write tap_migrations.to_json
         end
 
-        context "to a cask in an other tap" do
+        context "to a cask in another tap" do
           # Can't use local-caffeine. It is a fixture in the :core_cask_tap and would take precedence over :new_tap.
           let(:token) { "some-cask" }
 
@@ -149,6 +149,26 @@
           end
         end
 
+        context "to a formula in another tap" do
+          let(:token) { "some-cask" }
+
+          let(:old_tap) { Tap.fetch("homebrew", "foo") }
+          let(:new_tap) { Tap.fetch("homebrew", "bar") }
+
+          let(:formula_file) { new_tap.formula_dir/"#{token}.rb" }
+
+          before do
+            new_tap.formula_dir.mkpath
+            FileUtils.touch formula_file
+          end
+
+          it "does not warn when loading the short token" do
+            expect do
+              klass.for(token)
+            end.not_to output.to_stderr
+          end
+        end
+
         context "to the default tap" do
           let(:old_tap) { core_tap }
           let(:new_tap) { core_cask_tap }
diff --git a/Library/Homebrew/test/formulary_spec.rb b/Library/Homebrew/test/formulary_spec.rb
index 2063b4d412540..e0433f1886685 100644
--- a/Library/Homebrew/test/formulary_spec.rb
+++ b/Library/Homebrew/test/formulary_spec.rb
@@ -883,6 +883,27 @@ def formula_json_contents(extra_items = {})
           # end
         end
 
+        context "to a cask in a third-party tap" do
+          let(:old_tap) { Tap.fetch("another", "foo") }
+          let(:new_tap) { Tap.fetch("another", "bar") }
+          let(:cask_file) { new_tap.cask_dir/"#{token}.rb" }
+
+          before do
+            new_tap.cask_dir.mkpath
+            FileUtils.touch cask_file
+          end
+
+          after do
+            FileUtils.rm_rf HOMEBREW_TAP_DIRECTORY/"another"
+          end
+
+          it "does not warn when loading the short token" do
+            expect do
+              klass.loader_for(token)
+            end.not_to output.to_stderr
+          end
+        end
+
         context "to a third-party tap" do
           let(:old_tap) { Tap.fetch("another", "foo") }
           let(:new_tap) { Tap.fetch("another", "bar") }