Moore, whose dad Ronnie was fired from the Prenton Park hot-seat earlier in the summer, married his long-term partner during the summer and their three children all bear the name Thomas-Moore.
"It's the sensible thing to do. We've got three kids and they all have the Thomas-Moore name, so it wasn't a big decision," he told BBC Radio Merseyside.
"I spoke to my dad and mum and they gave me the okay, so it was pretty straightforward after that.
"I know it could cause a problem with the statisticians having to change all the details with the games I've played, but I think that's the only problem."