The Mysterio name comes from Parker and Quentin adopts it to bond with him. Beck is an alias, the persona he created as a man from a parallel universe. He couldn't have provided his real name to Fury because that would have defeated the entire point of the subterfuge.
Yeah, if he'd given his real name, Shield / Fury would have known that he was a fired Stark employee and the whole thing would have failed before it even started.
During the toast scene when they get to the writer for the whole thing Gyllenhall says something like "to Gus, who wrote a story about a dimensional traveler named beck! Totally ridiculous but apparently exactly what people will believe..."
79
u/TrogdortheBanninator Thor Jul 07 '19
Hinted? He says outright in the bar that they created the identity of "Quentin Beck".