Fill in the blank with the most appropriate word.
I asked her what her name was. "__________?" I asked her.
The two ways of relating what a person has said are 1)direct and 2)indirect (reported).
In the direct speech, the exact words of the original speaker are repeated.
In the indirect speech (reported speech), the exact meaning of what the speaker told is expressed but not necessarily in the speaker’s exact words.
Option A is correct as the indirect speech should be in the simple present tense.
Options B, C, and D are wrong as the speaker asked her her name the speaker is not asking someone else about the person whose name he wants to know, and the sentence structure is wrong respectively.
The correct answer is A)'What is your name'.