My name is Rynn. Just Rynn. Not Katherine. But ever since my ILs have met me, they have gotten the idea that my actual name is Katherine and Rynn is just a nickname. I have asked them not to introduce me or tell people it's my name but they always go back to it.
My husband and I took a small break from them when it continued and they apologized and seemed to be doing better. Then for my MILs birthday we were invited to celebrate with them and a couple of her friends came up to me and asked if I was Katherine. They said MIL talked all about me.
I decided to get a little bit jokey instead of annoyed and played up on it saying MIL is so forgetful and that I was so sorry she told them the wrong name. That I'll need to write my name on everything she owns so they don't forget. Her friends found it funny but told her it was weird that she gave them the wrong name.