what is the name of this outside faucet?
It's a typical Exterior Faucet Handle like these. This one happens to be Cello brand, but there's nothing special about it. That might not even be the original handle ;-) They tend to be pretty consistently standardized, so you should be able to use just about any kind of exterior faucet handle you can find.

This is what it looks like when it's off: 



As you can see, you really just need any kind of handle that will fit however that shaft is keyed, and a nut to hold it on.