The band had no name, this was a running joke on the series. They would be introduced as 'the band' and Al would say something like 'you guys really need to get a name'. The members were Richie, Potsie, Ralph, and Bag. Al and Chachi would play in the band in later episodes. http://www.sitcomsonline.com/happydays.html
http://www.sitcomsonline.com/happydays.html 