What are rain overshoes called?

Galoshes, also known as dickersons, gumshoes, or overshoes, are a type of rubber boot that is slipped over shoes to keep them from getting muddy or wet. In the United States, the word galoshes may be used interchangeably with boot, especially a rubberized boot. In the United Kingdom, however, a galosh is an overshoe made of a weatherproof material to protect a more vulnerable shoe underneath and keep the foot warm and dry.

The word comes through French "galoche" and Latin from Greek and originally meant a shoemaker's last; literally "wood" + "foot". By the 14th century it had been transferred to English style clogs, that is those with a wooden sole and fabric (e.g. leather) upper. By 1572 the term also applied to "a Gallage or Patten"; that is, an overshoe with a shaped wooden base to raise the wearer's good shoes off the ground.