USS Banhammer on my Fed PvP main. It was suggested by the regulars in the IRC channel.
IKS Ban'leth on my Klingon main. I believe Wishstone may have come up with the original name on that one, or maybe it was somebody else in the channel. It's the Klingon version of a banhammer.
USS Kearsarge on my Fed PvE main. I'm going cruisers, cruisers in Star Trek are traditionally named after the same historic sources as US Navy aircraft carriers, and my dad served on a real carrier by that name.
U.S.S. Valhalla. I used to run a Star Trek PBEM RPG a million years ago, and the ship the players were on was called the Valhalla, an Ascension class dreadnaught (basically, a refitted Constitution class with a third nacelle on top; it's over there on my profile pic). Those ships aren't cannon in the lore, so she will have to wind up being a plain ol' refitted Constitution, alas. Also, I'll name the Miranda class the U.S.S. Falcon, based off an even older game I ran. (When they were called Avenger class ships).