No matter what Bran Stark says, it’s pretty obvious that “The Winds of Winter,” the final episode of Game of Thrones season six, confirmed a long-held fan theory: that Jon Snow is the son of Rhaegar Targaryen and Lyanna Stark. The evidence came in the form of Lyanna whispering her child’s name to brother Ned, who agrees to raise him as his own. In case that wasn’t clear enough, the scene then seamlessly transitions from baby Jon to adult Jon.
HBO intentionally didn’t provide closed captioning for whatever Lyanna whispers to Ned, but according to Redditor “sparkledavisjr,” who has watched the Tower of Joy scene “about fifty times,” she didn’t say Jon. “I’m not a great lip-reader,” he wrote, “but I’m fairly certain what she says is Jaehaerys.”
It’s a name that probably isn’t familiar to non-book readers, because it’s only been mentioned once on the show, when Samwell is talking to Gilly during a forgettable scene in season three. Jaehaerys I Targaryen was the king of the Seven Kingdoms — the fourth Targaryen to hold such a title — approximately 200 years before the start of the series. He was dubbed “The Conciliator” or “The Wise.” A century and a half later, Jaehaerys II Targaryen became the 16th Targaryen to sit on the Iron Throne, and almost the last. That dishonor went to his son, Aerys II, better known as the Mad King, or Daenerys’ father.
If Lyanna was in love with Rhaegar (as seems likely), it makes sense for their son to have a Targaryen traditional name like his siblings Aegon and Rhaenys. Jaehaerys would be a good pick as the name isn’t associated with any real negative connotations, like Aerys, Maegor, etc. Not only is Jaehaerys the great-grandfather of Jon, he was the King who received the ORIGINAL PROPHECY about the prince who was promised from the woods witch with Jenny of Oldstones.
This prophecy is what caused Jaehaerys to force his children Aerys and Rhaella to marry, because it was prophesied that the [Prince That Was Promised] would be born of their line. Rhaegar was aware of this prophecy, and while he originally thought that he was the PTWP, he realized later he was not and that it would be one of his children. That is why he took/seduced Lyanna in the first place. His wife Elia could not have any more children, and he knew there must be a third child (The dragon must have three heads). (Via)
Ned couldn’t call the child Jaehaerys, though. That name’s as synonymous with the Targaryens as Cletus is to slack-jawed yokels. So Jaehaerys became Jon, possibly in honor of Ned’s friend and Hand of the King predecessor, Jon Arryn. Good thing, too: “You know nothing, Jaehaerys” isn’t nearly as catchy.