Thoughts from a fellow pup:

i believe you should be dressed or undressed only to the specifications of your Owner. So if He wants you dressed when posting a picture of yourself (which i wholeheartedly support) then that's all that matters.

As for pup names, it should be easy enough to get long lists of names from google even though some of them may be the traditional "fido" etc...

If you're asking for more self-reflecting names, then more information would do a world of good as to your likes, dislikes, pup-mannerisms, favorites, ...that kind of stuff. And, are you looking for humiliating/degrading names (slutpup) or names that you might actually name a dog (Rover)?

Regardless, right off the bat i like the names Roary, Cassie, Curios (emphasis on the 'o'), Amber, and Precious.

Good luck in your search for a name!