Agreeing with @Chancy here. It's easier to change name in UK passport now and have consistent name across all documents when establishing life in the US.
Otherwise, you'll have mismatch in multiple places. It'll take time and money to fix it. Not saying it's impossible, people do it all the time. I just find it a bit messy, and easily avoidable in your case.
Alternatively, can live with maiden name until you naturalize in the US, change your name in N-400 and then, update UK passport.
In my opinion only, it's easier to navigate through entire immigration process with one name.