Do it. They may not care and ignore you but you should try.
I don't have a questionable name. It's pretty obvious how it it said and spelled. It's pretty well known. For some reason my neighbours decided they didn't like my actual name and gave me another, just related to to my own, however I initially corrected them all the time and my husband always says my name slowly, clearly and loudly whenever he's outside having a chat over the fence.
Imagine my name is Maria. They have decided Marie is my name instead. But not just Marie. But Marie spelled completely wrong too, like Marree.
I write in the clearest, nearest primary school teacher way on Christmas cards and the like.
"From M a r i a, husband and kids"
And will still get "To Marree, husband and kids" on all cards.
I will also talk in the third person too whenever I can, saying things like, "And I was saying to myself, 'Oh Maria, don't forget the bins this week' And what did I do? Forgot them!"
They absolutely will not use my name and I don't know why. It's right there on my email, social media accounts and I even sign off texts to them with my name.
It took a while after moving in before I would use their names just to make sure I had the right ones.
So be prepared OP, you could correct them but I have no idea if it'll stick.