One of the most common things that trans and gender expansive folks do is change our names. Changing our name is often a way of living more into our authentic selves. Some change names in a very minor way - just a letter or two to change from one that is generally associated with one gender to one that is either more neutral, or associated more with another gender, and leave the last name alone.
Others, like me, completely change our names. My middle became my last. My first and middle names are completely different. I have different initials (although my first initial is the same.)
If you are in the process of changing your name, and you know you want to change only your first name, for instance, but don't know what name to pick, there are a number of strategies you might employ. First, is there a name that you've liked for a long time? One that has resonated with you for some reason? Is there a relative who was important to you, or helped you in some way? If you just let your mind wander into a space open to many names, what arises? What emotions arise when you consider one?
Ask loved ones how they think about what you are considering. Changing a name can be an arduous process administratively, so you do want to make sure you make the right choice. Spend some time imagining yourself as that name. See how that feels. What arises in you?
When I chose my name, I had had one in mind for many years. And I spent some time living with it myself, calling myself that name, and feeling the emotions that arose for me. Mostly, I felt joy and contentment. But there was an underlying fear. And when I dove deep into the fear, I realized it was a fear of being seen for who I was. That was more of an indication that I had chosen well.
One last note: it's worth googling your possible chosen full name early - just in case you happen to have chosen one that a famous (or infamous) person has, which could theoretically create problems for you in the future.