For me, the part that's hardest to suspend disbelief about is something different. I can buy an alternate world where Conan Doyle's detective fiction was never published. But it's hard to believe that anyone who bore a child in the late 20th century would've named them "Sherlock." It's a pretty weird name. But I suppose it's possible. There have been various historical figures with the last name Sherlock, and a few places with that name (in Australia and Kansas, though, not England). So I guess he could've been named after one of those.
As opposed to James Tiberious Kirk?