Probably the silliest thing I've done in naming my character was when I named one of my Fallout: New Vegas characters "Wheatley," and even gave him an Intelligence of 2 to complete the effect. I'm not comfortable with anything sillier than that, though. It just makes the game feel less complete most of the time, like me and my character don't belong there, and that's hardly good for the level of immersion I usually strive for.
On a side note, while you can't technically name the horses, I've taken to calling my horse in Skyrim "Boziik," which is Draconic for "bold." It's less because of how cool it sounds and more in honor of that one time I got attacked by a blood dragon and she ran up and started stamping on its face. Poor dragon didn't know what to do between me, my badass horse, and my companion.