There are also common surnames in Finnish, were the root word itself is considered as Finnish as possible, but etymology of the word is very obscure as these are not shared widely within Uralic family, or even within it's Baltic-Finnic branch. Currently most widely accepted hypothesis is that they are ancient substrate loans from now long extinct Paleo-European language(s) - Paleo-Lakelandic - spoken at Finland before Finno-Uralic speakers arrived to the Fennoscandia. These words are usually toponymic, which is the reason they are originally loaned in the first place. There are many etymologically very obscure place names in Finland.
For example:
Niemi 'cape' (Niemi, Nieminen, Niemelä etc. and as part of compound of wide variety of names, such as Kiviniemi, Leppäniemi, Vanhaniemi etc.
Saari 'island/isle' (Saari, Saarinen, Saarela, Saarioinen etc. and as part of compound of wide variety of names like Saarijärvi, Salosaari, Mustasaari etc.)
Musta 'black' (Mustonen, Mustola etc. and similarly a lot of compounds as above)