I think you do need to get your DH to have a word with them, for sceral reasons: he is their son, they will listen to him more. IMHO, if a parent or set of parents need dealing with over something awkward/shitty, the adult child of that parent tackles them, not the partner, but above all, because they might believe - or be kidding themselves - that DH actually agrees with them but doesn't want to say anything to you because he is under the thimb or besotted or whatever.
Some people do think that women change their names legally when they get married, as an earlier poster said. In fact, any woman who changes her name to her husband's is just adopting a false name, which is fine under UK law. Unless she changes it to his by deed poll, her real name will always actually be her maiden name.
I think they need putting straight about your surname, and about your job, etc. they clearly think very plain speaking is the order of the day towards you, so let them get a taste of their own medicine. After all, you're in the right here!
I'm presuming that you don't have kids yet, but you need to put your feet down, you and DH now, before they start taking thepiss on a whole new level when the DC come along.
You need to be confortable with making things awkward. If they tell you that that's not your real name when they are visiting tou, insist that they leave, as you will not be disrespected in your own home. If they mention this wrong name, ignore them, then tell them that's not your name when they ask why you're not responding. Just get up and walk away when they start this crap. Start calling them names that aren't theirs and tell them you're just doing what they do to you.
If it matters this much to you - and it would do me (my PILs spelling my name wrong and insisting that it should be spelt that way (not a name with variables, either!) drives me to the brink, so I feel for you!) - then PLAY HARDBALL!