Season 6 of Game of Thrones took Jon Snow on a journey of extremes: in just ten episodes, he went from corpse at Castle Black to King in the North, ruling from the childhood home he never thought would belong to him. And his ascendance to kingship wasn't the only big thing to happen to Jon in the Season 6 finale: there was finally confirmation of the long-held fan theory that Jon's true parents were not Ned and some mystery woman, but Ned's sister Lyanna and Targaryen prince Rhaegar. Despite dropping this information bomb on the audience, the show still played coy on a few facts. Lyanna whispered a few secrets into Young Ned's ear post-birth, such as the name of her newborn, but they were too quiet to hear. It opens up as many questions about Jon as it answers, such as: what is Jon Snow's real name?
A few of the things Lyanna said were clear. Though "his name is..." trailed off frustratingly, she did clearly tell Ned that if Robert found out about the baby, he'd kill him, and she pleaded for Ned to protect her son. Though Game of Thrones is withholding Jon's true name for more revelations down the road, that hasn't stopped fans on forums from coming up with some pretty convincing possibilities for brand new King Jon Snarkgaryen. The Targaryen royal family liked to reuse names over and over again, making it fairly easy to guess which ones might reassert themselves over time.
A popular theory has Prince Rhaegar attempting to recreate the three heads of the dragon by naming each of his children after one person in the historical Targaryen trio: Aegon, Rhaenys, and Visenya. In true Targaryen fashion, Rhaenys and Visenya were both King Aegon I's wives and his sisters. Rhaegar did name his first two children after his ancestors, but because Visenya is traditionally a woman's name, he could have given the male version of it to his third child, Jon, which could make Jon's real name Viserys. Somehow I don't think it suits him.
Other possible theories include names gleaned from the Targaryen family tree: Aegon, Aemon, or Jaehaerys. It may seem strange for Rhaegar to name two of his sons Aegon, but George Foreman named all five of his sons George, so it can happen. It would also make Jon work as a feasible nickname for Aegon, so it feels a little less like rewriting Jon's whole identity. However, that may be the point; Reddit user Eastwinter points out that "Jon Snow" sounds an awful lot like "John Doe," which functions as a placeholder name until someone's real identity can be confirmed.
Aemon has some narrative support to go off of, too. In A Storm of Swords, Jon mentions while playing as a child with Robb, he would pretend to be Prince Aemon the Dragonknight. In A Game of Thrones there is the line, "The gift of a sword, even a sword as fine as Longclaw, did not make him a Mormont. Nor was he Aemon Targaryen," which would be nicely ironic if it turns out that that is indeed Jon's birth name. Jon was also always very close to Aemon Targaryen of the Night's Watch, giving the name all kinds of importance in Jon's story.
Jaehaerys has less support, other than it sounding like an ostentatious Targ version of the name Jon. However, Jaehaerys I bears a passing similarity to Jon as a character. According to Reddit user MultiAli2, Jaehaerys had to fight to get the throne like Jon will likely have to do, and he helped out the Night's Watch at one point. Though he was a fairly skilled warrior, King Jaehaerys sought peace above all else, and Jon has been shown to try and broker peace between peoples before.
But whatever Jon's real name is, rest easy that at least it isn't Albus Severus.