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To preface this, I am going off the word of my grandmother, Anja Sihvonen.
Her understanding of the name Sihvonen was that is was relatively common (although this does not seem to be the case, Sihvonen is a relatively uncommon last name in Finland and is increasingly rare abroad), and it was her impression that the surname originated from a profession similar to a smith or craftsman. This is the only conjecture I have to go off of the meaning of the surname.
The "nen" part of the surname indicates that Sihvonen is the product of a clan or clans that originated in Eastern Finland. Thanks to this website, it is certain that most of the history of this last name surrounds the area of Jaakkima, a municipality on Lake Logoda in the Republic of Karelia (Karjala)- a region that once belonged to Finland but was ceded to Russia following the Winter War.
In my research I will do my best to uncover more of an understanding of the surname, but this is all of the information at hand presently.
-Holt Aarne Sihvonen