Depends on what version of Yubikey Mt. Gox is using. The latest version can store two passwords. Go to the Yubikey site, download the Yubikey manager software (available for Linux), and check to see how many slots you have available. I was able to store a 32-character password on the second slot of the Yubikey I received for a specific vendor. Just be careful not to overwrite the existing slot, or you may not be able to recover your Yubikey.
MtGox use both slots.
You can reset your Yubikey to use whatever you like, however doing so will break MtGox logins until you update the key that's stored on their end - and I don't think they've any motivation to do that whatsoever (particularly if you got the yubikey for free).