Well it's possible to some extent. Triper's correct, the server sends the mob's name to the client and his idea of showing up the name of the mob is actually a nice one!
There is, obviously, issues with the method. You can't show the name below the mob, because if you zoom out it'll show under the floor and you won't see it. Showing it above works fine, except if you zoom in and out, the text will change size as well. For example :

If that solution is fine with you, I can make these for all available sprites, just let me know! (On a side note, adding the name above the sprite is rather straightforward and it's done via a script xD!)