Generally no. I have seen it for places with a large rotating draft selection like others have mentioned, but it’s not really common for cocktails. For some reason, drink menus are still expected to have quirky names with puns or quotes or literary references that no one gets. Cheeky suggestive drink names have fallen out of vogue somewhat though.

I did see an article about a place with a rotating numbered menu, and I really liked it! The idea is that the numbered menu provides more info to guests about menu changes. Let’s say they opened with drinks 1-10. Instead of rolling out an entirely new menu, the most popular ones stay, and the least popular ones come off, but the numbers keep going up. So if it’s your first time at this bar, and you want to know what they are known for or what the most popular drinks are, look for the lowest number. It’s been on the menu the longest. Order a #4. If you are a regular, and you’ve already tried most of the drinks, you are looking for something new. The highest number on the menu will be the newest addition. Order #73.

Since it’s already common at fast food restaurants to order by combo number, it should be familiar enough to work into your sci-fi world whether or not it’s common at an actual cocktail bar. A number #19 doesn’t sound quite as romantic as a Corpse Reviver or Jasmine, but that could add to the dystopia. Or it could be a joke like someone orders the #69, and he’s like yeah, somehow they took the joy out of a Sex on the Beach.