Why The Name?
The name comes from the cocktail of the same name "Four Jokers". A lot of shirley's shipnames revolve around cocktails due to them being an alcoholic drink.
How did they get together?
Shirley's story revloves around them being a BFB contestant. They end up with Four as a result of just being around them for prolonged periods. Four becomes fond of and even fascinated with Shirley over their (literal) fragility and eagerness to spend time with him. They are constantly being broken and recovered by him and in the end stay with him for the BFB split and even after they end up in the exit.
How Are They Now?
Four's clingy and possessive over Shirley and Shirley's a weirdo for them LOL. They love to feel wanted and the two of them are usually side by side.
Now whos that baby..
That's Flask! They came about when Shirley asked Four about kids and they quite literally just pulled out this suddenly sentient Flask. Shirley doesn't question how or why they made them. But they're a happy (maybe dysfunctional) family.