Hampton Fancher and David Webb Peoples
The first screenwriter hired to work on Blade Runner was a dude named Hampton Fancher, who is known primarily for… writing Blade Runner. That's his one major screenwriting credit. Fancher pumped out a first draft, but when the filmmakers wanted re-writes, he started taking an excessively long amount of time. That's when they called in David Webb Peoples, who made lots of changes and ended up playing a crucial role in crafting the script.
Peoples has had a longer writing career than Fancher: he helped write the apocalyptic time-travel flick 12 Monkeys (1995) as well as the '80s fantasy Ladyhawke (1985); he also wrote the script for Clint Eastwood's classic Unforgiven (1992) and for the pseudo-Blade Runner semi-sequel Soldier (1998). Monkeys and Soldier have a lot in common with Blade Runner, since they both involve dystopian sci-fi visions of the future.
Peoples and Fancher sent the film through various name changes, as well—from Mechanismo to Dangerous Days (the producer Deeley's suggestion) to Blade Runner. Peoples got a major assist from his daughter, Rita, who came up with the term "replicants" to refer to the movie's androids—the term "replicant" isn't used in Philip K. Dick's book (source).
One final note: although Fancher and Peoples' did a classy job, one of the movies most famous lines was actually improvised by Rutger Hauer, the actor who played Roy: "All those ... moments will be lost in time, like tears... in rain" (source).