What does Dāmoclēs mean in Latin?

Dāmoclēs, a proper noun, means “Damocles”.

What is the genitive of Dāmoclēs?

The genitive singular is Dāmoclis. Dāmoclēs is masculine, third declension.

In classical Latin, [ˈdaː.mɔ.kɫeːs]; in ecclesiastical (church) Latin, [ˈdaː.mo.kles].

proper noun · masculinethird declension

Dāmoclēs m sg (genitive Dāmoclis)

Classical[ˈdaː.mɔ.kɫeːs]Ecclesiastical[ˈdaː.mo.kles]

Damocles
Dāmoclēs erat Argīvus, adulēscēns maiōris animī quam cōnsiliī, quī prīmō iūre iūrandō interpositō dē praesidiō expellendō cum idōneīs conlocūtus, dum vīrēs adicere coniūrātiōnī studet incautior fideī aestimātor fuit.59 BCE – 17 CE, Titus Livius, Ad urbe condita 34.25
Fortūnātus sibi Dāmoclēs vidēbātur106 BCE – 43 BCE, Cicero, Tusculanae Disputationes 5.62.2

Dāmō^cles, is, m.,

I. a courtier of Dionysius the younger, Cic. Tusc. 5, 21, 6 (cf. Hor. Od. 3, 1, 17; Pers. 3, 40).

Borrowed from Doric Greek Δᾱμοκλῆς (Dāmoklês); cognate with Attic Greek Δημοκλῆς (Dēmoklês).