'What's her name?'
 

Would 彼女の名前は何ですか be correct if I'm asking casually? Sounds wordy.

Yes, it's right. You could even drop the は何ですか　to sound more native, but it's whatever.



And I've always been under the inpression that 彼女 refers to something slightly on the side of "girlfriend"

Anyone agree?

I always thought 彼女 was for she... But referring to someone as "ぼくの彼女" would obviously make them "your girl" or like "your sweetheart"

Yeahhhhh, i see, i see.

If you're asking casually, that isn't a good way. It's completely grammatically correct, I assure you, but you wouldn't hear a native speaker say that even if you lived 200 years.　It sounds very "translated".

「あのこ名前なんなの？」

「あのこの名前なに？」

「あのこの名前知ってる？」 <--- Most natural even though it translates into "Know what her name is?"

Say only the last sentence with a rising intonation.

Nagoyankee, how do you feel about
あのこの名前は？

Thanks, I appreciate the help!

That is good if the speaker is nearly 100% sure that the listener knows what the girl's name is.

I am surprised we haven't seen

あのこ,誰？
Who's that girl?

あのこは誰か知っている？
Do you know who that girl is?

Slightly different meaning, as it is asking not the name, but "who"...but