diff --git a/message/output/email/classes/task/send_email_task.php b/message/output/email/classes/task/send_email_task.php
index 08c4e6843ab..ddad9842d8a 100644
--- a/message/output/email/classes/task/send_email_task.php
+++ b/message/output/email/classes/task/send_email_task.php
@@ -57,7 +57,7 @@ class send_email_task extends scheduled_task {
      * Send out emails.
      */
     public function execute() {
-        global $DB, $PAGE;
+        global $DB, $PAGE, $SITE;
 
         // Get the maximum id we are going to use.
         // We use this as records may be added to the table while this task runs.
@@ -91,7 +91,7 @@ class send_email_task extends scheduled_task {
             }
             $conversations->close();
             if ($hascontent) {
-                $subject = get_string('emaildigestsubject', 'message_email');
+                $subject = get_string('messagedigestemailsubject', 'message_email', format_string($SITE->fullname));
                 $message = $textrenderer->render($renderable);
                 $messagehtml = $htmlrenderer->render($renderable);
                 if (email_to_user($user, $noreplyuser, $subject, $message, $messagehtml)) {
diff --git a/message/output/email/lang/en/deprecated.txt b/message/output/email/lang/en/deprecated.txt
new file mode 100644
index 00000000000..4d2ad7501dd
--- /dev/null
+++ b/message/output/email/lang/en/deprecated.txt
@@ -0,0 +1 @@
+emaildigestsubject,message_email
\ No newline at end of file
diff --git a/message/output/email/lang/en/message_email.php b/message/output/email/lang/en/message_email.php
index 7290e0959b1..26cc0d8c17c 100644
--- a/message/output/email/lang/en/message_email.php
+++ b/message/output/email/lang/en/message_email.php
@@ -23,11 +23,11 @@
  */
 
 $string['email'] = 'Send email notifications to';
-$string['emaildigestsubject'] = 'Messages digest';
 $string['emaildigestunreadmessages'] = 'Unread messages';
 $string['emaildigestviewallmessages'] = 'View all messages';
 $string['emailonlyfromnoreplyaddress'] = 'Always send email from the no-reply address?';
 $string['ifemailleftempty'] = 'Leave empty to send notifications to {$a}';
+$string['messagedigestemailsubject'] = '{$a}: Messages digest';
 $string['pluginname'] = 'Email';
 $string['privacy:metadata:attachment'] = 'A file on the filesystem.';
 $string['privacy:metadata:attachname'] = 'The name of the attached file (extension indicates MIME).';
@@ -45,3 +45,5 @@ $string['privacy:metadata:subject'] = 'The subject line of the message.';
 $string['privacy:metadata:userfrom'] = 'The user sending the message.';
 $string['tasksendemail'] = 'Messages digest mailings';
 
+// Deprecated since Moodle 3.9.
+$string['emaildigestsubject'] = 'Messages digest';
diff --git a/message/output/email/tests/send_email_task_test.php b/message/output/email/tests/send_email_task_test.php
index ac6c8bc1cbc..b470603969b 100644
--- a/message/output/email/tests/send_email_task_test.php
+++ b/message/output/email/tests/send_email_task_test.php
@@ -43,7 +43,7 @@ class core_message_send_email_task_testcase extends advanced_testcase {
      * Test sending email task.
      */
     public function test_sending_email_task() {
-        global $DB;
+        global $DB, $SITE;
 
         $this->preventResetByRollback(); // Messaging is not compatible with transactions.
 
@@ -122,7 +122,8 @@ class core_message_send_email_task_testcase extends advanced_testcase {
         // Confirm it contains the correct data.
         $emails = $sink->get_messages();
         $email = reset($emails);
-        $this->assertSame(get_string('emaildigestsubject', 'message_email'), $email->subject);
+        $sitename = format_string($SITE->fullname);
+        $this->assertSame(get_string('messagedigestemailsubject', 'message_email', $sitename), $email->subject);
         $this->assertSame($user2->email, $email->to);
         $this->assertNotEmpty($email->header);
         $emailbody = quoted_printable_decode($email->body);