What does Panaetius mean in Latin?

Panaetius, a proper noun, means “a male given name from Ancient Greek — famously held by”.

What is the genitive of Panaetius?

The genitive singular is Panaetiī. Panaetius is masculine, second declension.

In classical Latin, [paˈnae̯.ti.ʊs]; in ecclesiastical (church) Latin, [paˈnɛt.t͡si.us].

proper noun · masculinesecond declension

Panaetius m sg (genitive Panaetiī or Panaetī)

Classical[paˈnae̯.ti.ʊs]Ecclesiastical[paˈnɛt.t͡si.us]

masculinesingulara male given name from Ancient Greek — famously held by
masculinesingularPanaetius, an Ancient Greek Stoic philosopher of the Hellenistic period.

Pănaetĭus, ii, m., = Παναίτιος,

I. a celebrated Stoic, a native of Rhodes, the instructor and friend of Scipio Africanus the Younger, Cic. Off. 1, 26, 90; id. de Or. 1, 11, 45; id. Off. 1, 12; 3, 2, 7; id. Tusc. 1, 32, 79: Hor. C. 1, 29, 14; Vell. 1, 13, 3.

Borrowed from Ancient Greek Παναίτιος (Panaítios).