Summarize:

This is an easy way to shape your identity without legally changing your name. Whether you identify as Alexander or Alexandra, you can call yourself Alex. Samuel and Samantha can be called Sam. Jordan can easily become Jordy or Jordi. If nothing else, this can be a solid interim step while you think about a more permanent name change. You could ask them what they would have named you if you were assigned your correct gender at birth. Or you could ask them what they would name you taking your personality and gender identity into account. You could run names you've been thinking of past your parents, they've known you the longest and will know if they fit you best. Don't feel the need to cater to any rules or norms, and remember that you don't need to keep things close to what they've been. If there is a name to which you have always been particularly drawn, choose that name. You don't have to choose a name that is similar to your birth name. If your birth name is "Martin" and you are transitioning to female, you do not have to choose "Martha" when you have always loved the name "Laura". If your birth name is "Cecilia", you do not have to choose "Cecil" if you've always liked the name "Ashton". If you are going through a sex change, you may feel empowered to explore parts of your personality that you were afraid to embrace before. Think about the identity that you intend to cultivate, and choose a name that fits with your vision for the new you. You may have connotations about certain names: tough, sweet, adventurous, etc. Pick a name that helps you become who you want to become. Name yourself after someone inspiring. If you grew up idolizing Marilyn Monroe, don't be afraid to change your name to Marilyn.
Try out a gender-neutral nickname. Ask your parents. Choose a name that you love. Pick a name that suits your new identity.