Change the "Warning: [Display Name] is currently editing this post" message

Hi,

I have a site has a display name (the company name), but has multiple admins that shares that display name when publishing content to the site.

I would like however to inform the admins of the site, who is editing content at the same time, with a message that uses the users First & Last name from their profile, & not their display name, as this means nothing in this case.

I have found the code in the post.php file (wp-admin > includes > post.php), and changed it there, but of course this is not the best way of doing this.

Is there a way to do it from the functions.php file?