🔼The name Jannes in the Bible
The name Jannes occurs only once in the Bible, namely in 2 Timothy 3:8, where Paul refers to an otherwise extra-Biblical tradition of two individuals named Jannes and Jambres, who opposed Moses but whose folly was made obvious to all.
Where this story comes from isn't clear but it most probably formed via the same folkloric mechanism that gave us the Book(s) of Enoch, and emerged from a fanciful expansion of the account of Moses and Aaron's showdown with the Egyptian magicians (Exodus 7:10-12).
Several Targums entertain the Jannes and Jambres spin-off, which appears to have included details of their ranks and business at Pharaoh's court, their joining the mysterious "mixed multitude" that evacuated Egypt along with Israel (Exodus 12:38), their generously offered assistance in manufacturing the golden calf (Exodus 32:4), their identification with the two otherwise unnamed servants of Balaam (Numbers 22:22), and their miraculous escape from the venging sword of Phinehas (Numbers 31:6-8).
The Cabbalists of the Middle Ages went even further and reported Jannes and Jambres forcing an unwelcomed entry into certain levels of heaven, where they encountered and defeated Michael and Gabriel but finally met their demise at the angelic hands of Metatron (that would be Enoch).
Surprisingly numerous references to earlier versions of these tales occur in Jewish and Roman literature, but are mostly post-Paul. Still, the Jewish scholar Artapanus of Alexandria already referred to it in the 3rd or 2nd century BC (cited by Numenius of Apamea in the 2nd century AD and in turn by Eusebius in the early fourth). The Roman historian Pliny the Elder, a contemporary of Paul, mentioned a Jannes along with Moses and someone named Jotape among famous Jewish magicians (Hist.31.11), and the Latin-writing Numedian (modern Algeria) Berber Apuleius listed Moses and Jannes among the world's great magicians.
Paul's reference to the story is by no means proof that he believed it to be historical. But his obvious appreciation for Stoic allegory makes it likely that he regarded it certainly useful for point-making. After all, in the same letter to Timothy, he writes his often misquoted statement that "all writing" (πασα γραφη, pasa graphe) is God-breathed and profitable for teaching (2 Timothy 3:16).
🔼Etymology of the name Jannes
It's not clear from which language the name Jannes is supposed to have been derived, but since his earliest literary application is as Egyptian priest, it could very well be Egyptian. But since Jannes appears to have originated as Jewish invention, his name might in fact be a Hebrew transcription.
In any event, the name Jannes occurs in Jewish literature mostly as יניס (Yanis) or יוחני (Yohanai), and the latter version quite clearly suggests that at least some Jewish scholars grouped the name Jannes together with names like John and Joanna, all deriving from the verb חנן (hanan), meaning to be gracious:
The Hebrew transliteration יוחני (Yohanai) suggests that the first part of our name comes from יה (Yah) = יהו (Yahu) = יו (Yu), which is the truncated form of יהוה, which is YHWH, the Name of the Lord, but if that were true we would have seen a signature ω in the Greek spelling of our name: Ιωαννης (Joannes).
More probable is that the יו-part of the Hebrew spelling is due to a modern (post-Biblical) transliteration of Ιαννης (Jannes), which in turn could be construed as the Hellenized reflection of an active form of our Hebrew verb חנן (hanan).
All things considered, it's no longer clear from which original the name Jannes was derived, but the way we have it our name is most probably the same as יחנן (yehanan), which would literally mean He Will Be Gracious or He Is Gracious.
But taken together with the name Jambres, which possibly reflects a want of excess, the name Jannes possibly reflects the common human weakness to want to obtain resources and comfort for very little effort. In that sense the name Jannes means Gratis or For Free.