Using the inscriptinal evidence, we get:

full(h)ugi

Add the pre-reformation sources:

fullmóþr (OS fulmodh 1476) - no other evidence.

Inscriptional evidence:

forkuþr : forsiáll (dubious - forsihl inscribed) - no other evidence.

Inscriptional evidence:

foldarr

Add the pre-reformation sources:

foldheiþr (woman foldheid in Agdir 1403, folldeid Hardnger 1439)

Runic:

fróþmarr (fruþmar)

But _post-reformation_:

fróþarr (1740-50 froder Ringarike, froer Vestfold and Sandshverve)

I'll make an exception here, as this post-reformation name has more
than one source _and_ I find it hard to imagine that any such ON
name as *fróþarr could have been invented after the reformation ;)

Runic:

froþolfr (runic fraþulf) : fraþi & fraþa (2 cases of the short form
for masc. names in fraþ-)

Saga-literature:

fraþmarr (alternative to fróþmarr perhaps, but a parallel stem of
the same meaning, compare Gothic fraþ-)

Runic none, saga-literature 2:

fiorleifr : fiorleif - no other sources

Runic:

fiolvarr (fiuluar, fiuluars) : fiolmóþr (fiulmuþ)

Saga-literature:

fiolviþr : fiolmundr (both about the same person) - dubious

Pre-reformation sources:

fiallarr (Agdir & Hardanger 1300-1378, OS fiæller 1413-43) :
fiallgeirr (Island 1234-1390)

Saga-literature:

falgeirr - no other sources

Runic:

forolfr/ulfr : farþegn : farmaþr : farbiorn : fari

Add the pre-reformation sources:

farfastr : fargeirr : farmundr : farmóþr - that's it, folks.

fari short-form of mascs. in far-. So:


full(h)ugi : fullmóþr : forkuþr : *forsiáll : foldarr : foldheiþr :
fróþmarr : fróþarr : froþolfr : fraþmarr : fiorleifr : fiorleif :
fiolvarr : fiolmóþr : fiolviþr : fiolmundr : fiallarr : fiallgeirr :
falgeirr : farfastr : forolfr : farþegn : fargeirr : farmundr :
farmóþr : farmaþr : farbiorn

26 plus 1 dubious

As far as I know, there are no other ON compound names beginning on
the letter f in ON, besides fránmarr, fríund and possibly fiolnir,
if we are to interpret that as a man's name in some cases. fróþi is
also short for names in fróþ- (2 above, compare fraþi).

-K