Good morning,
OK, to narrow it down a bit: in the broader area covered by the Atlas of Slovenia I found (probably missed some too):
3 representatives each have
DOG (Pasja ravan, Pasji hrib 798 Gabrovka, Psica 1769 Storžič)
EAR (V. and M.Ušje near Rombon; Ušinje hill 606 Il.Bistrica, Ušje 1821 Trenta)
4
OX (Volnik 546 Repentabor, Volovica 1455 Pohorje; Volovja reber, Volovljek).
SNAKE (Kačarjeva glava Kanin; Kačja rida 419 Straža; Kačji rob 1575 Ratitovec; Kačnik 500 Kras),
THRUSH (Jerebica/Monte Lago, Jerebičje 1761 Matkov kot; Jerebikovec Tromeja; Jerebikovec Mežakla),
HEN (Kokoš 674 Lipica, Kokošinjek 276 Semič, Kokošinjica Pokljuka, Kokošji hrib 514 Ambrus),
COW (Kravja črna gora Kobla, Kravjek 720 Pivka, Kravnjak 438 Rogatec-Đurmanec, Kravski hrib 565 Žužemberk; plus two more I saw in Friulian Dolomites: Monte Vacca and Vaccaliza.
HEN (Huhnerkogl/Košenjak 1522 on Kozjak, Kurešček 724 Krim, Kurica near Vernar, Kurjica 623 Javorniki)
LYNX (four Risnjaki near the border in Gorski Kotar)
ROE DEER (Srnavica 777 Radenci on Kolpa; Srnjak 918 Kalce – Hrušica; Srnjak 918 Planina; Srnski vrh 710 Žužemberk)
5
CHAMOIS (Gamsovke in Košuta ridge, Bovški Gamsovec, Dovški Gamsovec, Gamsov skret, Gamsova špica near Špik)
BADGER (Jazbec 980 Krim, Jazbečev vrh 698 Ravbarkomanda, Jazben vrh 925 Javorniki, Jazbina 604 Dobrova, Jazbić 1014 Gorski Kotar)
HARE (Kapunar 1050 Kobansko; Kunški vrh 871 Kočevje, Zajčev vrh 971 Trnovski gozd, Zajčji hrib 499 Kozina, Zajčnik 1746 Karavanke)
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PIGEON (Golobar Bovec, Golobičevec 790 Kalič, Golobja peč 1367 Virnikov Grintovec, Golobinjek 461 Straža, Golobov vrh 1072 Trnovski gozd, Golobovec 437 Muljava).
CRAB (Kranjski rak 1029; Rakov Škocjan; Rakov vrh 365 Kuzma; Rakova špica 2545 Škrlatica; Rakovški grič 646 Rakov Škocjan; Rakov rob 1207 Velika planina)
PIG (Na svinjah 867 Krn; Svinja planina; Svinjak (Bovški Matterhorn); Svinji hrib 1077 Racna gora; Svinjski grič 505 Kočevje; Svinjski vrh 509 Žužemberk)
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CHAMOIS (Košutica; Košuta Veliki vrh, Košutnikov turn, Mala Košuta, Košutna, Košutnik 592 Grgar, Tolsta Košuta
14 animals remain, after which even more peaks are named. We guess these.