You absolutely have the right to choose a name that is yours, not a bequest from your parents. There are more options than you might think: You could go by a surname, and most of those are derived from trades rather than gender roles. I've known two different gender-queer folks who simply went by "Red", so some adjective like that which describes your appearance or your soul could work. (A single letter could also work, as with "V" in Cyberpunk 2077) And of course there *are* gender-neutral names -- it's not coincidence that I go by "Robin" even though I *currently* tend to only present as masc.
For understanding friends, you could also have multiple names, that reflect your day-to-day variations. You could, for example, be Tina when presenting feminine, Tony when presenting masc, and T when it's too much trouble to be either.
But the only real recommendation I have is to not limit yourself, and to give yourself time to choose what works for you.