I only choose my own if I don't like the names they give me. I chose Super K for Wendy, and I wish I had said no to Chief calling me "kid" because I hate it sooo much ;-;
Not really "Cute" but when Ribbot was in my town he started calling me A-bomb, which was awesome. I was like, yes. Because I blow up and leave a huge radius of death and destruction. Spread the fear of my name. >: D
Most of the nicknames they suggest (at least in the American version) are just so bad. Everyone always talks about how they give them such cute or cool names and mine are always suggesting ones that are just garbage. Schmoopy was a recent one...lol nope.
So most times I have to make suggestions so I don't have to see such ugly nicknames.
Cookie started calling my mayor pop star which I thought was kinda cute but she calls me something else now. Hopper started calling me pop star too though, and I find it hilariously cute since he has those red angry eyes. I think my favourite nicknames I've gotten in the past are june bug and chickpea!