The logo is similar to that of Family Dollar or Dollar Tree, which are real life low-cost dollar stores. The name is also a pun on "dollar bills". Since the Dollar Pills store in Davis is based off of a real Rite Aid store in the roughly same location, along with similar colours, it can be assumed Dollar Pills is based off of Rite Aid.
Throughout the game's progress, you may find Patrick McReary and a friend of his armed with a gun pointing it at a victim during a Random event. You can choose him to be in your heist crew, or kill him.