I found this website that lists a bunch of Irish names, including a lot I've never really seen before. I went through all of the A-F names, and these are the ones I found most interesting of the names I hadn't heard before.
M
Accobrán, Acobhrán (A-kav-rawn) possibly a translation of Desiderius
Adamrae, Ámhra (AV-ra) "very wonderful"
Affiath (AF-ee)
Amargein, Aimirgin (AV-ir-in) "born of song"
Cáemlug, Caomhulú (KAYV-lu) "beautiful, beloved" + Lug ("light, brightness")
Cathmáel, Cathmhaol (KOH-vel) "battle-champion"
Causantín, Consaldín, Cansandín (kow-SAD-in) Constantine
Cithrúadh, Ciothruadh (KIR-oo-ah)
Cléirech, Cléireach (KLER-ach) "clerk, cleric"
Daigre, Daighre (DAY-ree) "flame, fire"
Dúnacán, Dúnagán (DOON-a-gawn)
Eolang, Eolann (O-lan)
Faíltigern, Faoiltiarn (FEL-tiarn)
Feoras (FOR-as)
Féthchú (FEY-koo)
Finguine, Fionghuine (fin-EEN-a) "kin-slayer" :(
Fínnechta, Fínsnechta, Fínneachta (FIN-acht-a)
Finnlug, Fionnlugh, Fionnlú (fin-LOO) Fionn + Lugh (the Manx version is Finlo)
Flannchad, Flannchadh, Flannacha (FLAN-a-cha) "red warrior"
Forannán, Farannán (FUR-an-awn)
F
Aghna (EE-na) possibly a form of Agnes (I actually have heard this one before and really liked it)
Aíbgréne, Aoibhgréine (eev-GRAY-na) "radiance of the sun, ray of sunshine" (I've previously discovered this, too)
Aibhne, Aibhne (EEV-nee)
Ainbthenm, Ainbthine, Ainfean (AN-fan) perhapd "storm, violence, fury"
Cáemnat, Caomhnait, Caomhnad (KAYV-nit) "beautiful girl"
Der Luca, Dar Luga, Dearlogha, Dearlú (dar-LOO) "daughter of Lugh"
Étromma, Éadroma (ayd-ROM-a) "lightheadedness, giddiness"
Fiadnat, Fiadhnait, Fianait (FEE-anit)
Fiamuin, Fiamain (FEE-a-vin)
Fíne (FEE-na)
Fínmed, Fínmhidh (FIN-vee) "wine-mead"
Finnétan, Finnéadan (fin-NEY-dan) "fair brow"
Finnmaith, Fionnmhaith (FIN-va) "fair, good"
Fínscoth (FIN-ska) "wine blossom"
Fodla, Fodhla (FOH-la) name for Ireland
Fuinche, Fainche (FIN-hee) Irish goddess of war
Any you like?
And if you know any further information, or have any corrections or anything to contribute to any of these names, I'd really appreciate it!