As a G Suite user and administrator can control how users can edit their profile information.
Use the Directory page settings to manage user profile changes. If you are getting an error message "To change your cover photo, contact your admin", do the following.
» Sign in as the your Google Suite Admin
» From the Admin console, go to Apps > G Suite > Directory.
» On the Directory page, click Profile editing > Choose to allow user editing for each of the following:
Name, Photo, Gender...
For more info click here.