Beck. It's a somewhat uncommon boys name, which can also easily be used as a substitute for the girl name Becky, which is short for Rebecca.
And her name here even has 'Bec' in it! 'Beck' is good, there's a singer called Beck iirc. I could only suggest 'Rab' or 'Reb'. It's unique!
Bex In one of the earlier seasons of Grey’s Anatomy there was a patient named Rebecca who turned out to be intersex and went by Bex.
Beck. First one that comes to mind. It's also a boys name, and is sometimes short for Beckham. It's a cute name.