grammar - Which is grammatically correct: "first and last name" or "first and last names"?

So I'm having a bit of a pluraltiy issue here, and I'm not sure which is the correct version because they both seem right, and I've seen both versions used in writing:

A. What is your first and last name?

B. What are your first and last names?

The second version seems more grammatically correct than the first one, but it just sounds odd. The first one is what you'd typically hear in speech, but that of course doesn't mean it's right.

Then again, this doesn't seem grammatically correct:

Your first and last name is ...

While this does:

Your first and last names are ...

So is one of these more right than the other, or are they equally valid?

EDIT: Option A previously said "What are your first and last name" when it should have said "What is your first and last name". My question is about the pluralization of "name".

Answer

More broadly, one might consider four possibilities:

A. What is your first and last name?

B. What is your first and last names?

C. What are your first and last name?

D. What are your first and last names?

Of these,

A is the right choice if you only need one full name,

B is ungrammatical,

C is ungrammatical (One might think that the distributive property, X Z + Y Z = (X + Y) Z applies here, making "first and last name" equivalent to "first name and last name", which is plural. However, "first and last name" is singular)

D is not ungrammatical, but is less idiomatic, and may be construed as requesting multiple names (such as aliases),