These names we use, these titles really, are important. So however someone wants to use them, I think, should be respected. Yes, hubby and I say Wife or Hubby instead of 'my' now. We dropped the possessive while we were in the beginnings of poly and learning to get our own mind around the differences between choosing to be together and owning. Now it's a title. Capital letter W Wife. Capital letter H Hubby.
However, what we call people differs on the people. My mother, for example. I often slip and refer to her simply as Nana. Why? We decided the kids would call her nana as soon as we found out we were having kids. She was never a mother, (unless Mommie Dearest counts), so she doesn't get the term GRANDmother. You need to be a mother before you get grand. My mother in law who for a few short years was more of a mother to me is grandmother, my grandmother who helped raise me and took me in was the bousha. (Polish I think? It's what we grew up calling her as well.)
So the names are important, they are like titles you are given/earn. For some, things like Husband, Mother, Father, Friend, are important and so they use them and use MY to show that title was actually earned. For others My Friend, is a simple way of saying it's someone I know and don't despise.
So I dont' really think the MY is necessarily ownership, it may just be part of the title!
Me: Late 30s pansexual poly.
DH: My husband of 19 yrs and father of 3 teen girls.
DC: LDR of +4 year