The oldest name for it is closh and the name it had prior to being croquet was pall-mall.

Of course in order to play croquet you need a stretch of green space and the name of the game of pall-mall is what gave the alley where it was played its name.

Pall Mall, which cuts through the capital's center, probably got its name because British nobility was fond of playing "paille maille" on long, straight streets.