What does nōmen gentīle mean in Latin?

nōmen gentīle, a noun, means “nomen, the family name of an ancient Roman, indicating the person's gens”.

What is the genitive of nōmen gentīle?

The genitive singular is nōminis gentīlis. nōmen gentīle is third declension.

In classical Latin, [ˈnoː.mɛn ɡɛnˈtiː.ɫɛ]; in ecclesiastical (church) Latin, [ˈnɔː.men d͡ʒenˈtiː.le].

nounthird declension

nōmen gentīle n (genitive nōminis gentīlis)

Classical[ˈnoː.mɛn ɡɛnˈtiː.ɫɛ]Ecclesiastical[ˈnɔː.men d͡ʒenˈtiː.le]

historicalnomen, the family name of an ancient Roman, indicating the person's gens
Numerio certe adjecto, cujus nominis forma prorsus gentilis est, quo antiquior librarius erat, eo magis mirari debebat eundem hominem duo nomina gentilia habuisse.1848, Wilhelm Francke et al., Index scholarum publice et privatim in academia Georgia Augusta per semestre aestivum anni MDCCCXLVIII, habendarum kalendis Majis incipiendarum per dies a IV. usque as IX. Septembris finiendarum, University of Göttingen, page 7:

From nōmen + gentīle (nominative neuter singular of gentīlis: "of the gens").