Although the final episode of Game of Thrones season six, “The Winds of Winter,” revealed the identity of Jon Snow’s mother as Lyanna Stark — and not some random southern woman as Ned Stark claimed — it didn’t actually confirm who the father was. Most fans are pretty comfortable making the assumption that Rhaegar Targaryen is Jon’s papa (because come on, he totally is) but as nothing has been 100% confirmed, we can’t say for certain that this is the case. Thankfully, one dedicated viewer has found evidence from the finale that heavily supports the R+L=J theory.
During the finale’s Tower of Joy scene, HBO deliberately didn’t provide closed captioning during the part where Lyanna whispers something to Ned, but Redditor “sparkledavisjr” claims to have figured out at least one important word that was spoken. He says he’s watched the scene “about fifty times,” and while he admits that he’s “not a great lip-reader,” he does write, “but I’m fairly certain what she says is Jaehaerys.”
If you’re thinking that Jaehaerys sounds like a Targaryen name, you’d be correct. The name has only been mentioned once before on the show, during a throwaway scene from season three when Samwell is telling Gilly about some Westeros history. Jaehaerys I Targaryen was the king of the Seven Kingdoms about 200 years before the start of the series. He was known as “The Concilator” or “The Wise.” There was another, Jaehaerys II Targaryen, who was the 16th Targaryen to sit on the Iron Throne and was the grandfather of Rhaegar and Daenerys.
Here’s a more in-depth explanation:
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)
Obviously, Ned couldn’t just go ahead and start calling Lyanna’s child Jaehaerys, as that would have been a dead giveaway as to his true heritage. Plus, what kind of Stark rolls with a three syllable name, anyway?