One consideration is, do you like your letter? That is, the first letter of your birth name. I do, so I've kept it. If you have that restriction, it's easier to narrow down to a short list of options that you can just try out on various people you meet until one of them feels good.
The most important thing, as Stef Sanjati said, is to pick a name you are comfortable with. So, for me, while Leila and Cecilia are great, Jenny just feels like home. So that's the choice. (Unless I suddenly change my mind.)