Avatars and Names are completely separate elements, so I’m not sure what you mean.
If a member has not added an image to their avatar / profile, then the system defaults to using a letter (the first letter of their username) in a coloured background to identify them, so that this relates, in a small way, to that user, so we are already doing what you are suggesting.
If you want to control the name on the site, then there is a related topic here:
Please do consider searching the resources on this site for lots more information