Going by a new name question

Hi everyone. I've been out (mostly) as non binary for years, but these past few months I decided I wanted to go by a new name, something that felt like me rather than what I'm just called. And while it feels nice to be me with this name it's still new and I feel... weird, I guess, telling people that is my name when it's not legally changed as my name. Did or does anyone feel like that? Like that's me, that's who I want to be, and I love the name. But putting it out there, even to strangers, there's just a moment of hesitation. I'm trying to push past it but for some reason the legality of it is making me nervous