I know a wheelie is when the front wheel is in the air but does it have a different name for when the back wheel is in the air?
It has many different names. Its usually called a stoppie or nose manual. Lots of people also call it a "fakie", but that term is more common in skateboarding. Some people refer to it as an "endo" but that's usually used to refer to a crash where you go over the handlebars. Other names such as nose rides, front wheelies, tip ups, and tip rides are used, but its pretty rare that someone calls them that.