Would the job title be voice actor or voice actress if the person is a female? Is it false to call yourself a ''voice actor'' when you're ?

i wouldnt say its false, just go with whatever you prefer. you can use voice over artist for more gender neutral, voice actress for female, and voice actor has become more general

As language has become more gender-neutral, actor now refers to a person who acts rather than men only.

It is not false.  Actor is not gender-specific when used as a generic term, any more than mankind is.

Both male and female could be called an actor but only females are called actresses.

how about "voice over artist"?

I'm not sure why you think this question is different for a voice actor than other kinds of actor. The trend now is to avoid gender-specific names for occupations, but the terms actor and actress are so well established that it sounds strange to call a woman an actor. "Marilyn Monroe was a famous actor"? I don't know about that.

get off this gender kick