What should be the entry element of the name Yits.ha.k b.R. Mena.hem Monish ha-Kohen, zal, mi-Druis.k?

The forename "Manish" or "Monish" often goes with "Menahem," so it would be better to treat it as a forename here.  Making a ref from it as a surname is fine.

Whether "ha-Kohen" should be treated as a surname or a $c is a trickier question.  The practice is to treat it as a $c for a
pre-20th-century author, unless there's evidence the other way.  In this case, there IS evidence, namely the treatment in Bet 'eked.  Bet 'eked carries a lot of authority, since it's a reference source in the author's language of activity, so it's recommended to adopt its view of the surname (and entry-element) status here.

ID:NAFR9932301     ST:p    EL:n   STH:a    MS:n   UIP:a    TD:19991019013731 KRC:a    NMU:a    CRC:c   UPN:a   SBU:a   SBC:a   DID:n    DF:10-14-99       RFE:a CSC:c  SRU:b   SRT:n   SRN:n   TSS:n   TGA:?   ROM:?   MOD:  LCT:      VST:d 10-21-99
010    nr 99032301
040    CSt-HCbengcCSt-HC
100 1  Hakohen, Yits.ha.k ben Mena.hem Monish
400 0  Yits.ha.k ben Mena.hem Monish,$cha-Kohen, mi-Druis.k
400 1  Monish, Yits.ha.k ben Mena.hem,$cha-Kohen
400 0  Isaak Monish
670    Sefer Li.ku.te Yits.ha.k, 1891:$bt.p. (Yits.ha.k b.R. Mena.hem Monish ha-Kohen, zal, mi-Druis.k) t.p. verso ( ... Isaaka Monysha [in Cyr.])
670    Bet 'e.ked sefarim, 1951-1956$b(hdg.: Hakohen, Yits.ha.k)
675    Ency. Judaica, c1972.