This is so weird!!
My first thought is to wonder if the father might have something internal that causes him to act this way (like autism).
But sometimes adults - even sometimes well-meaning adults - try to "joke around" with children in a way that just doesn't work. A friend of mine had a teacher in elementary school who developed a habit of always referring to my friend by a rhyming name (like if my friend's name was Suzy, this teacher was calling her "Suzy Doozy", etc). And this teacher only did that to my friend, not to anyone else in the class. It irritated my friend, so she told her mother. Her mother reached out to the teacher and that put an end to it.
You certainly should address this. I think the best way is either to reach out to the mother or reach out to the mother and father *together*. I think either an in-person conversation (when your daughter is not nearby) or an email are both fine ways to handle it.
Additionally:
It might be interesting to find out "why" this started, if there is a reason beyond just "the father being weird".
For example, if your daughter is eating grapes and he says "Your name is grape-head, right?", that might be something he says to his own children to be "silly".
Or, maybe something related to "names" happened at that party you missed - for example, maybe your daughter introduced herself to the father, and now for some reason he thinks it is funny to pretend to not remember her name.
I remember once when I was very young I introduced myself to an adult by my first and last name ("Hi, I'm ChaCha Doe" rather than just "Hi, I'm ChaCha"). This adult then made a point of *always* bringing up my last name in conversation, in sort of an over-the-top way. Apparently that adult thought my way of introduction was funny (maybe thought it was precocious). That became irritating!