There are many stories of how Fozzie Bear got his name.
It's sometimes thought that Fozzie Bear was named after his performer, Frank Oz. Other sources generally say he was named in honor of master puppet-builder Faz Fazakas. Frank Oz has claimed the name Fozzie Bear is a variant off of "fuzzy bear". Other sources claim that Fozzie was originally going to be called "Ozzie Bear"; however when there were potential legal problems with the name "Ozzie," it was changed to Fozzie. The true origins of Fozzie's name are unknown.
The old Henson.com website, had an "Ask Henson" feature that contained these responses to the origin of Fozzie's name being connected to Frank Oz:
“According to Muppet writer Craig Shemin, Frank Oz insists that Fozzie Bear was not named for him. In fact, Fozzie originally was going to be called "Ozzie Bear." Fortunately for us, there were some legal problems with using the name "Ozzie," so the bear needed a new name. Ultimately, he was renamed "Fozzie" as a tribute to puppet-builder Faz Fazakas.”
“There are a couple of answers to your question, depending on who you ask. Fozzie Bear's name is generally considered more of an homage to Faz Fazakas. Mr. Fazakas is an electro-mechanical wizard who designed many of the technological innovations which enable the Muppets to be more realistically animated. Fazakas created the ear mechanism which permits Fozzie to wriggle his ears. Additionally, Frank Oz contends that Fozzie's name is a play on the "fuzzy" nature of a bear. Either way, although it might seem that Fozzie is named for his performer, his name has a different origin.”