I think you should just alter and not change your present first name. Simply make it Will instead of William. I would however not touch the middle name.
I know I have this thing about bible parallels quotations but bear with me. We all have our quirks. Great book by the way :) You know Jesus gave Simon the surname Peter and later on he was mainly called that name, so it cant be all that bad to make a name change along the way.
14 And he ordained twelve, that they should be with him, and that he might send them forth to preach, 15 And to have power to heal sicknesses, and to cast out devils: 16 And Simon he surnamed Peter; (Mark 3, 14-16)