The name wasn't specific, and the word "gay" was not used, because being gay was illegal in every state, with penalties ranging up to life in prison. Being caught with a "gay" book in your possession would not only get you arrested, it would give the police a complete list of places to raid.
It was wallet-sized, so you could carry it in your pocket without being detected, and dispose of it quickly if necessary.
Later editions included codes:
G: Girls (Lesbians)
M: Mixed gay/straight
M/S: Mixed crowd
P: Private club
PE: Pretty elegant
RT: Raunchy types (hustlers)
S: Shows ("record pantomine acts with female impersonators")
SM: Some motorcycle.
YC: Young crowd.
The edition I bought at the adult bookstore in Bloomington in 1982 used the word "gay," and listed bars, bookstores, theaters, and bathhouses. I carefully calculated which city in the U.S. was best for gay men by weighing all four (in my naivete, I didn't realize that the bookstores and theaters were erotic).
New York got the most points.
By the 1980s, The Damron Guide was illustrated with steamy ads.
Bob Damron died in 1989, but his annual guidebook is still going strong, specializing in international travel.