"native or inhabitant of Finland; a member of the Finnic race," Old English finnas, from Old Norse finnr, the Norsemen's name for the Suomi. Some suggest a connection with fen. Attested in Tacitus as Fenni. Finlander in English is from 1727.
"drink laced with chloral hydrate," by 1918. Mickey Finn was used from the 1880s as the name of the main character in a series of popular humorous Irish-American stories published by New York Sun staff writer Ernest Jarrold (1848-1912), who sometimes also used it as his pen-name. Perhaps there is a connection.
U.S. underworld slang sense of "$5 bill" is 1925, from Yiddish finif "five," from German fünf (from PIE root *penkwe- "five") and thus unrelated. The same word had been used in England in 1868 to mean "five pound note" (earlier finnip, 1839).
Siberian Mongolian people, 1580s, from Russian samoyed (11c.), traditionally literally "self-eaters," i.e. "cannibals" (the first element cognate with same, the second with eat), but this might be Russian folk etymology of a native name:
The common Russian etymology of the name Samoyed, meaning "self-eater," deepened the Russians' already exotic image of far-northerners. The most probable linguistic origin of Samoyed, however, is from the Saami — saam-edne, "land of the people" [Andrei V. Golovnev and Gail Osherenko, "Siberian Survival: The Nenets and Their Story," Cornell University, 1999]
Which would make the name a variant of Suomi "Finn." The native name is Nenets. As a language name by 1829. As the name of a type of dog (once used as a working dog in the Arctic) it is attested from 1889 (Samoyed dog).