I had decided that Cheez-It would be what Chadder called me. Our personal special nickname. But now for some reason, literally the entire island is calling me that! Anytime someone would ask if they could also call me that, I would say no. Obviously Cheez-It only makes sense and is cute and funny because he is a mouse that looks like cheese! I have special nicknames with villagers and they use them in conversation, but they also use the Cheez-It too as if it's as big of a deal and on the same level as my actual name (if that makes sense?). How do I get everyone to stop calling me Cheez-It?!
That’s how nicknames work, unfortunately. It’s like a trend. They pick it up FAST. You can just go to Isabelle and complain to her about every villager that you don’t like the way they talk. I believe that will change their catchphrases. You’d have to do it one by one, though, which requires a bit of patience.
At first, I enjoyed nicknames, but as OP mentioned, it gets awkward when a villager-specific nickname catches on with others. In the end, I ultimately told villagers to just use my own name. It is just simpler and less jarring while playing.