My mayor is Rafael. One of his nicknames is R. The others are: lil' guy; kid; bucko; youngin. A couple of villagers call him "my little youngin" or "my kid".
Yuu-shii started getting passed around Wishfall and I don't even really remember who started it. I believe it was Whitney that I told to call me Yuu-shii, and then pretty much all my villagers started asking if they could use it, too. Plus, the way the snooty voice sounds, I can actually hear when Whitney says "Yuu-shii," to the point where if my roommate is playing and I hear my name, I can ask him if he's talking about me.
Ankha asked me for a nickname so I just imput my standard Russian nickname and it spread. I'd tell you what it is but then you could really easily find out what my real name is. xD