If you like your name (Eli), then stick with it.
I could be wrong as I don't know the full story with your tutor, but did she know you as a female first and then later as a male? Or did you come out to her?
My thinking is, if she sees you as female, then she might think others see you as female too. Because she saw Eli as "Ellie" and possibly thinks of you as a girl, then she probably thinks other people will read it, look at you, and think the same way she does.
Which is all a load of crap. You definitely pass, bro. Eli is a strong, masculine name and I think it suits you.