Pour me a drink, will you?
Python 3, 693 690 686 687 bytes

Yeah, naive approach. I tried some compression methods, and this one seems to be the shortest.

-2 bytes thanks to HyperNeutrino.

EDIT: Bug fixed.



import random
v="Absinthe$Death in the Afternoon$Earthquake$Green Russians$Green Vesper$Moloko Plus$Beer$Black and Tan$Black Velvet$Boilermaker$Michelada$Irish Car Bomb$Brandy$B&amp;B$Brandy Alexander$French Connection$Horse's Neck$Sidecar$Cachaca$Caipirinha$Leite de Onca$Quentao$Rabo-de-Galo$Royce$Gin$Bramble$Casino$Clover Club Cocktail$Gin Fizz$Martini$Rum$Bacardi$Cuba Libre$Daiquiri$El Presidente$Pina Colada$Tequila$El Toro Loco$Margarita$Matador$Paloma$Tequila Sunrise$Vodka$Black Russian$Bloody Mary$Cosmopolitan$Kamikaze$Screwdriver$Whiskey$Bourbon Lancer$Irish Coffee$Manhattan$Rusty Nail$Whiskey Sour".split('$');a=v.index(input());print(v[a-a%6if a%6else random.randint(1,5)+a])


Try it online!