What it is Yo, What's up!
Well, strangely enough, the two names can be equated, although not likely from a purely linguistic association. As discovered in the study of the Iliad and Aeneid, the hero Ascanius/Iulus/Julius was one and the same as Persian Darius and Egyptian/Libyan Osorkon V. The name Osorkon is in turn a variant of Issachar/Osiris (John).
Hebrew: Azariah (son of Hoshaiah)/Nabu-zaradan
Greek: Ascanius son of Aeneas/Ion
Roman: Iulus / Julius, Servius Tullius, Lucius-Quinctius, Cincinnatus
Libyan: Osorkon V (son of Sheshonq/Mentuemhet)
The name Julius however seems to have been derived from Troy (Ilios), "city of the gods". The battle of Troy was a game of king of the hill. So, the name Julius probably symbolized "King of the Hill", or Great King, which of course Darius ultimately became.
The name Julius has also been associated with the Roman god Jupiter, the Hebrew Joseph. It also connotes "hairy" in Greek. If that sense was intended, then the name might have originally associated more with the Esau/Geb typology.
Another name for John is Elijah, the Greek Elias, which has some resemblance to Ilus/Iulus. However, the association of Julius with John/Jannaeus may have been simply due to the regional identities of Darius as Iulus and Osorkon/Azariah.
I don't think we can connect Julius and John to the Greek Ion as Agamemron recently proposed. Ion was a Greek epithet of Joshua/Benjamin/David (Horus) rather than Eliezar/Issachar/Jo-Hanan/Azariah (Osiris). This is not to say that Horus figures did not sometimes get turned into Osirises and vice versa.
© Charles N. Pope, US Library of Congress. All rights reserved.