The oldest mentions of the name Tossavainen in Finnish church records are from the 16th century.
The "ancestral home" of the family is understood to be Tossavala Island in Jäppilä, Pieksänmäki (62°21'19.5"N 27°29'53.9"E).
There is also a Tossava Bay in the same region, at the north end of the Lake Nilakka (63°16'45.4"N 26°10'20.3"E).
The bit that was here before about Torshavn having anything to do with the name is totally bogus.