It's likely you're thinking of a specific type of small monkey, or perhaps a fictional character. Could you give me more information about what you're looking for?
What is the name of monkey size your finger?
There isn't a specific type of monkey that is the size of a finger. Monkeys come in a wide range of sizes, from the tiny pygmy marmoset (about the size of a mouse) to the large mandrill (up to 80 pounds).