Who is the Finn?

Finn is one of Daisy's household servants. He helps Nick set up his house for the visit between Daisy and Gatsby, helps pick out the food and the flowers, and so on, and so on!

The Finn is the Finnish woman Nick hired as his housekeeper/cook when he rented the house next door to Gatsby.

To reiterate, a Finn is a Finnish person, as in a person from Finland. "Finn" is not a name. We know the Finn is female because Nick refers to her as a her: "I had forgotten to tell my Finn to come back, so I drove into West Egg Village to search for her among soggy, whitewashed alleys and to buy some cups and lemons and flowers" (Fitzgerald). "My Finn" is just an endearing pet phrase Nick uses to refer to his servant.

I'm quoting from WordReference now: "Queen Victoria had a Scottish manservant she was very fond of. I wouldn't be surprised if she sometimes thought of him fondly as 'My Scot.'"