I've considered changing my name. If I ever decide to, then I'll legally be Casey Morgan {my surname}. I've joined non-trans forums as Casey and rather like it when people call me that online. As of right now nobody calls me Casey IRL but that will change soon. The next time my transgender support group meets they'll be calling me Casey (right now they know me as Mike) and using gender neutral pronouns.
I'll have to see how that goes. I mean, Casey fits me much better than Mike. But on the other hand, I'm not at a point where I feel I can "justify" telling my parents "thanks for the name and all but I like this one better".
If people are already calling you something gender neutral, I would imagine the transition would be easier all around. I guess too it also depends on how others see you. Most people see me as male, mostly because I haven't said anything to them. But if they see you as more gender neutral anyway, or closer to it, then that will help.
Then too, it's your name. If your current name makes you feel uncomfortable then that sounds to me like a good reason to consider changing it.