What does Sōphrosynē mean in Latin?

Sōphrosynē, a proper noun, means “Dionysius the Elder’s daughter”.

What is the genitive of Sōphrosynē?

The genitive singular is Sōphrosynēs. Sōphrosynē is feminine, first declension.

In classical Latin, [soːˈpʰrɔ.sy.neː]; in ecclesiastical (church) Latin, [soˈfrɔː.s̬i.ne].

proper noun · femininefirst declension

Sōphrosynē f sg (genitive Sōphrosynēs)

Classical[soːˈpʰrɔ.sy.neː]Ecclesiastical[soˈfrɔː.s̬i.ne]

Dionysius the Elder’s daughter
Dion, Hipparini filius, Syracusanus, nobili genere natus, utraque implicatus tyrannide Dionysiorum. namque ille superior Aristomachen, sororem Dionis, habuit in matrimonio, ex qua duos filios, Hipparinum et Nisaeum, procreavit totidemque filias, nomine Sophrosynen et Areten, quarum priorem Dionysio filio, eidem cui regnum reliquit, nuptum dedit, alteram, Areten, Dioni.ante 25 BC, Cornelius Nepos (author), Alfredus Fleckeisen (editor), De Vita Dionis in Cornelii Nepotis Vitae (1890), part X: “Dion”, ¶ 1, § 1, page 37

From the Ancient Greek Σωφροσῠ́νη (Sōphrosŭ́nē).