As has already been pointed out, in the days before television, movies and other visual media, people had no idea what the people they heard looked like. So, if you could do a passable imitation, you could probably gig as the "real" artist.
I've always been dismayed by having heard, from a number of sources, that Brownie McGhee (not one of my favorite guitarists) began his career passing himself off as Blind Boy Fuller.
Who would have been taken in by that deception?
Imposters exist to this day.
I've gigged, as a Bass Player, with two different, Sugar Pie DeSantos and I have no idea which of them was the real one. If, in fact, either of them were!
During the '80's, I often played Dobro and Harmonica, on the County Fair circuit with a guy who billed himself as, Country Singer, Red Foley, despite the fact that Red Foley had been dead for many years.
I guess the entertainment industry is built on BS and Hokum and the imposters certainly prove that point.