Using the inscriptional evidence, we get:

finnviþr : finnolfr/ulfr
(plus fiþr/finnr - a non-compound name)

Using saga-literature, we get:

finnvarþr : finngeirr : finnalfr : finnbogi : finni : finna

finni and finna are short-forms for masc. and fem. names in finn-,
respectively.

Not much progress yet, so we add pre-reformation non-saga sources:

finnketill/kell : finngarþr : finngerþr : finnbiorn : finnmundr :
finnlaug : finnleikr

Progress, indeed. finnleikr was an earl in Scotland around 1000
(finnleikr skotaiarl); the others present no problems. Here are some
Modern Icelandic constructions:

finnfríður : finndís : finnbjörg

We also have a post-reformation *finnbergr (finnberg 1740-50 in
south-east Norway). Hmmm. The last 4 all look good and ancient, but
we lack pre-reformation sources for them. I'll let the readers look
more closely at these, while listing the pre-reformation sources:

finnviþr : finnvarþr : finnolfr : finnketill/kell : finngarþr :
finngerþr : finngeirr : finnalfr : finnbogi : finnbiorn :
finnmundr : finnlaug : finnleikr

13 plus one reconstruction: *finnelfr - mascs. in -alfr yield fems.
in -e,lfr in the other categories. *finnbiorg would be likely, but I
have no *finnsteinn, even though there is a finnbiorn, and *-laugr
would be logical, but mascs. are so much rarer against feminines in -
laug that I won't take the chance. So, 13 plus 1 reconstruction.

-K