diff --git a/app/main/views/templates.py b/app/main/views/templates.py
index aa9ea60c9..6091488ad 100644
--- a/app/main/views/templates.py
+++ b/app/main/views/templates.py
@@ -318,7 +318,7 @@ def copy_template(service_id, template_id):
         return add_service_template(service_id, template['template_type'])
 
     template['template_content'] = template['content']
-    template['name'] = 'Copy of ‘{}’'.format(template['name'])
+    template['name'] = _get_template_copy_name(template, current_service.all_templates)
     form = form_objects[template['template_type']](**template)
 
     return render_template(
@@ -330,6 +330,20 @@ def copy_template(service_id, template_id):
     )
 
 
+def _get_template_copy_name(template, existing_templates):
+
+    template_names = [existing['name'] for existing in existing_templates]
+
+    for index in reversed(range(1, 10)):
+        if '{} (copy {})'.format(template['name'], index) in template_names:
+            return '{} (copy {})'.format(template['name'], index + 1)
+
+    if '{} (copy)'.format(template['name']) in template_names:
+        return '{} (copy 2)'.format(template['name'])
+
+    return '{} (copy)'.format(template['name'])
+
+
 @main.route("/services/<service_id>/templates/action-blocked/<notification_type>/<return_to>/<template_id>")
 @login_required
 @user_has_permissions('manage_templates')
diff --git a/tests/app/main/views/test_templates.py b/tests/app/main/views/test_templates.py
index e2e0cdc0c..bfa8c511a 100644
--- a/tests/app/main/views/test_templates.py
+++ b/tests/app/main/views/test_templates.py
@@ -823,11 +823,44 @@ def test_choose_a_template_to_copy(
     )
 
 
+@pytest.mark.parametrize('existing_template_names, expected_name', (
+    (
+        ['Two week reminder'],
+        'Two week reminder (copy)'
+    ),
+    (
+        ['Two week reminder (copy)'],
+        'Two week reminder (copy 2)'
+    ),
+    (
+        ['Two week reminder', 'Two week reminder (copy)'],
+        'Two week reminder (copy 2)'
+    ),
+    (
+        ['Two week reminder (copy 8)', 'Two week reminder (copy 9)'],
+        'Two week reminder (copy 10)'
+    ),
+    (
+        ['Two week reminder (copy)', 'Two week reminder (copy 9)'],
+        'Two week reminder (copy 10)'
+    ),
+    (
+        ['Two week reminder (copy)', 'Two week reminder (copy 10)'],
+        'Two week reminder (copy 2)'
+    ),
+))
 def test_load_edit_template_with_copy_of_template(
     client_request,
+    mock_get_service_templates,
     mock_get_service_email_template,
     mock_get_non_empty_organisations_and_services_for_user,
+    existing_template_names,
+    expected_name,
 ):
+    mock_get_service_templates.side_effect = lambda service_id: {'data': [
+        {'name': existing_template_name, 'template_type': 'sms'}
+        for existing_template_name in existing_template_names
+    ]}
     page = client_request.get(
         'main.copy_template',
         service_id=SERVICE_ONE_ID,
@@ -838,7 +871,7 @@ def test_load_edit_template_with_copy_of_template(
     assert page.select_one('form')['method'] == 'post'
 
     assert page.select_one('input')['value'] == (
-        'Copy of ‘Two week reminder’'
+        expected_name
     )
     assert page.select_one('textarea').text == (
         'Your ((thing)) is due soon'