The latter. The choice of name may have been chosen to help the character seem more relateable to those watching, but it could be a coincidence. I do think, Burnham's experience will be a form of allegory, growing up among people who do not accept how you feel you really are, despite your species/gender.
I would like at some point that the actress or producers explain why they went with a male name as opposed to a female name or feminine version of it.
I know it is sometimes used for a girl's name, but it is an unusual choice and I'm curious about it.