I believe this is a form of possessive dativ (assuming that this is the right name in english...). Basically, with this form you would say for instance: “To the consul is great courage” instead of “ The consul has great courage”. Translated that would be: “Magna virtus est consuli” as opposed to “Consul habet magnam virtutem”.
However, I also believe that in this case “Quid est nominem suum?” should be grammatically correct.
Edit: corrected consuli.
There's no such word as "nominem"*.
"Suus" describes something belonging to the subject. In the question "quid est nomen?" the subject is "quid", so if you were to say "quid est nomen suum?" that would mean you are asking about the name of "quid". This of course would make no sense at all.
- except for a form of the verb "nominare": "nominem" is something like "let me name".
True about the first point! Thanks! I have corrected it in my previous post.
Concerning the second part of your post, that possessive dative is the only thing which came to my mind, so yes: the ad litteram translation would be “what is the name to him/her/it?” as far as I can see... Then again,I might be wrong...