diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7142d2aff43..c259d9f562e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,10 @@
 
 ## master (unreleased)
 
+### New features
+
+* [#7619](https://github.com/rubocop-hq/rubocop/issues/7619): Support autocorrect of legacy cop names for `Migration/DepartmentName`. ([@koic][])
+
 ### Bug fixes
 
 * [#7639](https://github.com/rubocop-hq/rubocop/pull/7639): Fix logical operator edge case in `omit_parentheses` style of `Style/MethodCallWithArgsParentheses`. ([@gsamokovarov][])
diff --git a/lib/rubocop/cop/migration/department_name.rb b/lib/rubocop/cop/migration/department_name.rb
index b3ff4c0f9f6..e79f69f03e3 100644
--- a/lib/rubocop/cop/migration/department_name.rb
+++ b/lib/rubocop/cop/migration/department_name.rb
@@ -35,8 +35,13 @@ def investigate(processed_source)
 
         def autocorrect(range)
           shall_warn = false
-          qualified_cop_name = Cop.registry.qualified_cop_name(range.source,
+          cop_name = range.source
+          qualified_cop_name = Cop.registry.qualified_cop_name(cop_name,
                                                                nil, shall_warn)
+          unless qualified_cop_name.include?('/')
+            qualified_cop_name = qualified_legacy_cop_name(cop_name)
+          end
+
           ->(corrector) { corrector.replace(range, qualified_cop_name) }
         end
 
@@ -53,6 +58,14 @@ def check_cop_name(name, comment, offset)
         def valid_content_token?(content_token)
           !DISABLING_COPS_CONTENT_TOKEN.match(content_token).nil?
         end
+
+        def qualified_legacy_cop_name(cop_name)
+          legacy_cop_names = RuboCop::ConfigObsoletion::OBSOLETE_COPS.keys
+
+          legacy_cop_names.detect do |legacy_cop_name|
+            legacy_cop_name.split('/')[1] == cop_name
+          end
+        end
       end
     end
   end
diff --git a/spec/rubocop/cop/migration/department_name_spec.rb b/spec/rubocop/cop/migration/department_name_spec.rb
index 257fec3de82..8c4fead6049 100644
--- a/spec/rubocop/cop/migration/department_name_spec.rb
+++ b/spec/rubocop/cop/migration/department_name_spec.rb
@@ -53,6 +53,23 @@
         # rubocop : enable Style/Alias, Layout/LineLength
       RUBY
     end
+
+    it 'registers offenses and corrects when using a legacy cop name' do
+      expect_offense(<<~RUBY, 'file.rb')
+        # rubocop:disable SingleSpaceBeforeFirstArg, Layout/LineLength
+                          ^^^^^^^^^^^^^^^^^^^^^^^^^ Department name is missing.
+        name             "apache_kafka"
+      RUBY
+
+      # `Style/SingleSpaceBeforeFirstArg` is a legacy name that has been
+      # renamed to `Layout/SpaceBeforeFirstArg`. In the autocorrection,
+      # the department name is complemented by the legacy cop name.
+      # Migration to the new name is expected to be modified using Gry gem.
+      expect_correction(<<~RUBY)
+        # rubocop:disable Style/SingleSpaceBeforeFirstArg, Layout/LineLength
+        name             "apache_kafka"
+      RUBY
+    end
   end
 
   context 'when a disable comment has cop names with departments' do