The term "finish" is incorrect when referring to people from Finland. The correct demonym for people from Finland is "Finnish."
The reason people from Finland are called "Finnish" is rooted in the English language's historical development. Over time, certain terms and names for nationalities have evolved and become standardized through common usage and historical influences.
In the case of Finland, the English term "Finnish" is derived from the Old English word "Finnas," which referred to the people of Finland. The Old English word likely had its origins in Old Norse, where "finnr" was used to denote the people of Finland.
As languages evolve, the spelling and pronunciation of words can change, but the demonym "Finnish" has remained consistent in English to describe people from Finland. So, while it might seem similar to "finish," they are distinct words with different meanings and origins.