baby's surname

I wasn't sure which group to post this in, anyway my son has my surname as his dad didn't want to be around so he's not on his birth certificate, has never even seen him or anything, we broke up just a few weeks into the pregnancy as he was becoming violent, anyway I'm getting married next year and my fiancée has basically taken on the role of dad, he came to every appointment, scan, was there for the birth etc, anyway I'd love to change my sons name to his, how would I go about this? I'm in the UK