diff --git a/config/default.yml b/config/default.yml
index 0b888553efd7..5fac0a0aa0fa 100644
--- a/config/default.yml
+++ b/config/default.yml
@@ -685,11 +685,12 @@ Naming/PredicateName:
 Naming/UncommunicativeBlockParamName:
   # Parameter names may be equal to or greater than this value
   MinParamNameLength: 1
+  AllowedNames:
 
 Naming/UncommunicativeMethodArgName:
   # Argrument names may be equal to or greater than this value
   MinArgNameLength: 3
-
+  AllowedNames:
 
 Naming/VariableName:
   EnforcedStyle: snake_case
diff --git a/lib/rubocop/cop/mixin/uncommunicative_name.rb b/lib/rubocop/cop/mixin/uncommunicative_name.rb
index f6db26f865f2..509e76a25d3f 100644
--- a/lib/rubocop/cop/mixin/uncommunicative_name.rb
+++ b/lib/rubocop/cop/mixin/uncommunicative_name.rb
@@ -12,6 +12,7 @@ module UncommunicativeName
       def check(node, args, min:)
         args.each do |arg|
           source = arg.children.first.to_s
+          next if allowed_names.include?(source)
           range = arg_range(arg, source.size)
           case_offense(node, range) if uppercase?(source)
           num_offense(node, range) if ends_with_num?(source)
@@ -63,6 +64,10 @@ def arg_range(arg, length)
                                   begin_pos,
                                   begin_pos + length)
       end
+
+      def allowed_names
+        cop_config['AllowedNames'] || []
+      end
     end
   end
 end
diff --git a/spec/rubocop/cop/naming/uncommunicative_block_param_name_spec.rb b/spec/rubocop/cop/naming/uncommunicative_block_param_name_spec.rb
index 6ab7f3c8adf0..56955f9e814b 100644
--- a/spec/rubocop/cop/naming/uncommunicative_block_param_name_spec.rb
+++ b/spec/rubocop/cop/naming/uncommunicative_block_param_name_spec.rb
@@ -1,6 +1,6 @@
 # frozen_string_literal: true
 
-describe RuboCop::Cop::Naming::UncommunicativeBlockParamName, :config do
+RSpec.describe RuboCop::Cop::Naming::UncommunicativeBlockParamName, :config do
   subject(:cop) { described_class.new(config) }
 
   let(:cop_config) { { 'MinParamNameLength' => 2 } }
@@ -61,4 +61,25 @@
       'Only use lowercase characters for block parameter.'
     ]
   end
+
+  context 'with AllowedNames' do
+    let(:cop_config) do
+      {
+        'AllowedNames' => %w[foo1 foo2]
+      }
+    end
+
+    it 'accepts specified block param names' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        something { |foo1, foo2| do_things }
+      RUBY
+    end
+
+    it 'registers unlisted offensive names' do
+      expect_offense(<<-RUBY.strip_indent)
+        something { |bar, bar1| do_things }
+                          ^^^^ Do not end block parameter with a number.
+      RUBY
+    end
+  end
 end
diff --git a/spec/rubocop/cop/naming/uncommunicative_method_arg_name_spec.rb b/spec/rubocop/cop/naming/uncommunicative_method_arg_name_spec.rb
index acb1df03454c..dcad8dc487c6 100644
--- a/spec/rubocop/cop/naming/uncommunicative_method_arg_name_spec.rb
+++ b/spec/rubocop/cop/naming/uncommunicative_method_arg_name_spec.rb
@@ -1,6 +1,6 @@
 # frozen_string_literal: true
 
-describe RuboCop::Cop::Naming::UncommunicativeMethodArgName, :config do
+RSpec.describe RuboCop::Cop::Naming::UncommunicativeMethodArgName, :config do
   subject(:cop) { described_class.new(config) }
 
   let(:cop_config) { { 'MinParamNameLength' => 3 } }
@@ -112,4 +112,29 @@ def self.something(y, num1, oFo)
       'Only use lowercase characters for method argument.'
     ]
   end
+
+  context 'with AllowedNames' do
+    let(:cop_config) do
+      {
+        'AllowedNames' => %w[foo1 foo2]
+      }
+    end
+
+    it 'accepts specified block param names' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        def quux(foo1, foo2)
+          do_stuff
+        end
+      RUBY
+    end
+
+    it 'registers unlisted offensive names' do
+      expect_offense(<<-RUBY.strip_indent)
+        def quux(bar, bar1)
+                      ^^^^ Do not end method argument with a number.
+          do_stuff
+        end
+      RUBY
+    end
+  end
 end