A Finn is a person from Finland. Write it with a capital F when it means that. The adjective and the language are Finnish, not Finn: you can say “She is a Finn” or “She is Finnish,” but “Finn language” is not how people say it. Though actually, the old northern word behind Finn did not start as a neat label for today’s country. In Old English the Finnas were people of the far north, and the name was used for the Sami; the Old Norse word finnr may first have meant a hunter-gatherer, perhaps a ‘finder’ of food. The country name Finland kept that old word. You do not need this history to use Finn correctly now — it just means someone from Finland — but it is why the tidy modern map and the old word do not match perfectly. Separately, Finn is also a given name (from Irish Fionn, “fair”). That name is a different story; do not mix the two origins.