Oh, don't get me started on her psyche... She's pretty messed up :p
Maybe easiest to understand: Everyone she grew up with, familiy, friends, everyone she knew, all hated what she is. The first two and a half decades of her life she was pretty much brainwashed into the same hatred. She was also brainwashed into loving and working for a country and agency she trusted that 1. no longer exists and 2. sold her out for financial benefits.
In short, the only reason all the people she's ever loved, trusted or cared about don't want her dead is, that they all believe she died almost half a century ago.
So yeah, she's stuggled with quite some self-loathing and probably still has a quite disturbed self-image.
First psychological reason for not wanting people to know she's an elf, among many other things, is that it's a first barrier between the outside world and her inner self. As long as they don't know her, they can't get close to her and they can't hurt her.
On the field though, she simply enjoys the fact that people underestimate her when they see a 20-something year-old girl, as evidenced by Netzgeist original post. No need for them to realize she's got more experience than any of them.