There are many stories of the origin of the term 'monkey dish', but none of them are verified. Here are a few of them:
It is a bowl the size a monkey would use.
It is a bowl that was originally made from a monkey's skull.
It is a shallow bowl the size of a monkey's hand.
Royalty once had small portions of their food fed to monkeys to be sure it wasn't poisoned.
Bell hops wore caps similar to those worn by organ grinder monkeys. The bell hops became known as 'monkeys,' and the smaller dishes were used by these 'monkeys' to serve in-room guests.
The list goes on.