Before settling on Blade Runner, the filmmakers considered a number of titles. Apparently, the title of Philip K. Dick's book Do Androids Dream of Electric Sheep? was never really on the table: too long. Originally, Hampton Fancher, one of the screenwriters, wanted to use the title Mechanismo. Yeah, cringe. The producers rejected it, and one of them, Michael Deeley, suggested Dangerous Days. Yet that wasn't to everyone's satisfaction, either.
Finally, Fancher found a screenplay by the famous beat writer, William S. Burroughs, entitled The Bladerunner, which was itself based on a book called The Bladerunner,by Alan Nourse. In these works, a "blade runner" wasn't a cop tracking down biological androids but "a person who sells illegal surgical instruments."
None of this had anything do with the plot of the movie, of course, but it sounded pretty cool, so Ridley Scott bought the rights to the name, and Fancher and the other screenwriter, Peoples, redefined Deckard's job description as that of a "blade runner" (source).