I've been having the same awkwardness going about integrating my new name too. Mine shortens to something gender-neutral, and even though I went through a good bit of reflection coming up with it, there's still that nervous feeling like I could have made a better choice.
But hey, if it's something people around you are open to talking about, then I think it'd be good to introduce it as tentative. People are really very empathetic if you introduce your though processes along with your ideas.
I got used to my chosen name by using the gender-neutral form at work, and by applying it to video game avatars and online usernames (and doodling it on my homework). By the point I wanted to introduce it to others as a transitioning name, I already responded to it. I knew it referred to me. It'd feel weird not to keep it, at this point. I think it's something you kind of have to break in.
