The single most common name for the Blade Runner handgun, is simply the blasteror the Detective Special.
Both can be traced back to one of the biggest name in BR blaster prop game: Richard Coyle. During the 1970's Coyle was building mail-order rayguns, and was hired by the Star Trek II: TWOK production prop department. He founded his own prop company in the early 1980's, and work on films like The Last Starfighter. Since around 1997, Richard Coyle has been turning out some of the most accurate (and expensive) copies of the BR blaster.
In various interviews, Coyle called the weapon the blaster or the 2019 Detective Special. His kits also carry the same names. Given his looming presence over the BR blaster community, these names carry a great deal of weight.
The Pflager Katsumata-D
One of the more interesting, older, and odd names attached to the blaster was Pflager-Katsumata series D or just PKD. The name PKD is a tribute to author Philip K. Dick and was one of the earliest name attached to the handgun just as the internet was taking off in the mid-1990's. The name pflager is an German last name, and was attached to the gun because it sounds cool . The other name, katsumata is a traditional Japanese last name, and could be a reference to anime director Tomoharu Katsumata.