Hello, Mo.Anwar, and welcome to the Grammar Exchange.
There are cases where the present is acceptable in reported speech, but I don't think this is one. Since it is obvious that a person's name does not change over time, there is no need to keep the present in this case. Quite the contrary, the past is required to bring the reader's or the listener's mind back to the moment when the question was asked:
- She asked what my name was.