Depending on your birth name, there are ways of incorporating it in your new identity if you don't want to lose it entirely. Getting a new legal identity is kinda crucial for a lot of legal matters though. If you're worried about raising suspicion from random people for perking up to the utterance of your old name, all you have to do is say someone really close to you was called that.
Personally, I'm not good at lying, so I tend to just tell people as much truth as I think they can deal with. Otherwise it can get complicated, and transitioning was mostly for me to be authentic to myself and others. But how open you are with others about your trans-status is up to you. But I think the name thing is relatively minor.
In my case, I'm keeping my old name as my first two initials, K and C. Even though I lucked out getting a non-gendered name, I want to have a legal separation from the male and female identity. This way, the family and friends I'm out to don't have to call me something new, as long as they use the right pronouns.
Hugs,
- Katie