I should think so. My wife didn't take my name when we married so maintains her maiden name on her passport and other legal documents but our bank were perfectly happy for us to have a joint account with my surname.
I know that isn't quite the same as what you are asking but it is the same principle.
It would depend what you are known as. If you are known to all and sundry as Mr and Mrs Smith then yes, if you are known to all and sundry as Mr Smith and Miss Jones then no.
If you can "prove" to the bank that your name is "A Smith" then you can have an account in that name, joint or individual. If you can't prove it then they won't let you because that is the law. Whether you call yourself Mrs, Ms or Miss (or maybe even Mr) is entirely up to you, it is only the names that matter. You can have a joint account with anyone, you don't have to share a name (or anything else for that matter!).