Took three of my small plants, and gave them each a new pot. I don't have very many small pots so for some of this it wasn't much of a move up, but I hope enough to keep them happier for a while. It's really better to repot in the springtime when they are putting out new growth; at that time I'll probably get some more pots of the proper size.
It's really a Swedish Begonia! Also called Swedish Ivy. I don't know much about begonias. But now that I've found a proper name for it, I can read up about its proper care. For example, I found out pretty quickly that it doesn't care for cholorine, so needs rainwater. Of course, another sensitive plant!
I'm still going to refer to it as Creeping Charlie, though, because that name is more familiar to me.