It will surprise no one that hermetically is derived from the name Hermes, but it doesn't come from the name of the messenger of the gods of Greek mythology,* at least not directly.
Hermes Trismegistus was a legendary alchemist, magician, and astrologer who was said to have been a contemporary of Moses. His name means "thrice great Hermes," as in three times as great as the original god.
Scholars argue about exactly who Hermes Trismegistus was, or if he was even a real person. A lot of research points to the possibility that he is some combination of the Greek god Hermes and the Egyptian god Thoth. But whatever he was or wasn't, a Hermetic cult grew up around his magical and alchemical teachings, which were recorded during the second and third centuries AD in the Hermetica.
One of the alchemical secrets in the Hermetica was a way to magically seal a container so that no air or other contaminants can get into it. Today we know that it doesn't take magic to do that, but the idea of hermetically sealing a container has stuck around.
* Not to mention the god of trade, thieves, travelers, sports, athletes, and border crossings, and the slayer of the hundred-eyed giant Argus Panoptes.