I think you have watched too many "Secret Squirrel" and "Morocco Mole" cartoons. Why would someone working for the FBI or CIA need an alias while in the US? Who would they be hiding from?
Are you sane and sober?.... Of course secret agents use false identities no matter where in the world they happen to be.
However your suggestion does display the gullible naivete of a trusting child. Lee Oswald was also gullible and naive...
When he was in Russia he was always on his toes,kept himself alert and on guard.... But he foolishly thought that he could relax when he returned home to the good ol USA. He was simply too naive to understand that there were Brigands and Bastards right here in the good ol USA, who would use him like a marionette...