folki and folka are just the short-forms for masc. and fem. names in
folk, respectively. Folkgeirr is somewhat dubious, as the
inscription reads fulkir (coulf be fylkir), but name -geirr names
show -kir, -ker, -kiz, -kez in younger Swedish inscriptions, while
older ones tend to show -kaiz. Given that a personal name *fylkir is
otherwise not attested, *folkgeirr is what most scholars would read,
as it belongs to a known name-category. Folkuþr is just a typical,
conservative West Norse version of the inscribed fulkaþr (uþr/aþr <
PN *folkôþuz). The name folkvarþr (or folkvorþr) is alone found
inscribed in West Norse (one time, against non elsewhere).
Using pre-reformation non-saga sources, we add:
folkviþr : *folkvin(r) : folksteinn : folkarr :
OS folkvidher; folkvinr OS (folkvin 1279-1421) OD(folkwin, folken),
but also OG folcwin, OE folkwine volken 1371-1687 - thus, the name
could, but need not be, a Germanic borrowing. folksteinn (OS folsten
1446), folkviþr (OS folkvidher, folvit 1283-1520 OGut fullkuiþr),
and folkarr OS (folkar 1385) OD (folker 1413-1645) OGut (folkar) are
are normal ON formations.
Using saga-sources, we add nothing, as names in folk- seem to have
been non-existent (or more probably more correctly, much rarer) in
West Norse areas. Combining our pre-reformation sources, we get:
8 names plus *folkgeirr, which while probably not fylkir, could be a
masc. equivalent to folkvé (*folkvér), even if written fulkir (on
this compare, for instance, þórir < þórvér beside þórvé, etc.), but
a resulting West Norse *følkir would be strange, and while fylkir
could result, it would run into the ON word fylkir, which is not a
personal name, as far as we can tell. On the other hand, *folkvér
would avoid having to reconstruct *folkvér, which would be the most
obvious reconstruction in view of folkvé. Any ideas or references
here would be appreciated. Lastly, a fem. *folkbiorg is a likely
reconstruction, based on folksteinn (same meaning) and folkbiorn
(while not cognate, mascs. in -biorn occur beside fems. in -biorg/
borg in other categories). I left folkvinr out as dubious, but it
could be actual for ON (compare auþunn < auþvinr).