It has no official name, though most people call it the "Gauntlet of Rassilon"
At the very end of the episode, we finally get confirmation that he is, indeed, Rassilon, when the Tenth Doctor calls him that. Rassilon is a name that appears occasionally in the classic series: he is the founder of the Time Lord society and one of their greatest inventors; he is largely responsible for everything the Time Lord technology is capable of doing.
Rassilon had a whole slew of powerful artifacts named after him, which he mostly invented himself, including:
- Rod of Rassilon
- Crown of Rassilon
- Coronet of Rassilon
- Seal of Rassilon
- Ring of Rassilon
Many of these artifacts were passed on to the sitting President of the Time Lords, and had important control functions related to running Gallifrey. Others, like the Ring, were so powerful they were hidden away. If you're interested, and can find them, most of the references to Rassilons tool belt are from the episodes The Five Doctors and The Invasion of Time (though the Seal of Rassilon is the thing Eleven sticks on Handle's head in Time of the Doctor to help him translate Gallifreyan).
The gauntlet he is wearing is most likely another item in this collection, probably crafted as a weapon in the Time War. To my knowledge, it was never referenced or named prior to The End of Time, and has not been named or referenced since.