Everybody knows Jon Snow’s lineage isn’t what Jon Snow thinks it is. He’s always believed that he’s the bastard son of Ned Stark and somebody or other, which isn’t true. He’s the son of Lyanna Stark and Rhaegar Targaryen. Everybody attributes a great deal of significance to this, and hopes he’ll be the next one to sit the Iron Throne. That he will be the one to save Westeros as the Prince That Was Promised, for his is the song of ice and fire. Alas, it ain’t true: Say what you want about his parentage, he’s not Jon Snow, but he isn’t Jon Targaryen either.
Jon Snow’s True Identity Isn’t Jon Targaryen, It’s Jon Sand
Where did Jon Snow get his name? Well, he got the name Jon from Ned (or possibly from Lyanna), and he’s named after Jon Arryn, Ned’s mentor, who warded him in the Eyrie and was the first to raise his banners in rebellion against the Targaryens. That’s the Jon part. The Snow part comes from being a bastard of the North.
But Jon isn’t actually a bastard of the North. It’s curious why he has that name in the first place, when you think about it: We know he was born in the South. We don’t officially know that Jon Snow was born in the Tower of Joy—a remote tower in the Prince’s Pass on the border of Dorne and the Reach, guarded by three members of the Kingsguard despite having no members of the monarchy there—but, I mean, come on. And if he was, he shouldn’t be Jon Snow… he should be Jon Sand. Or even better, Jon Flowers!!
Don’t go around calling Jon Flowers Jon Targaryen, either, though. Presumably he has the Snow moniker because Ned wouldn’t cough up the deets on where he was actually born, and because he was being raised in the North. But it’s not really the truth. But remember, we have no evidence to suggest that Rhaegar and Lyanna were married. The official tale of her being carried off has lots of holes in it, and it seemed like a consensual arrangement. But we have no reason to think they secretly married, even though that would be allowed under Targaryen tradition. If they didn’t, then Jon Snow is just Jon Flowers, just another bastard of the South, not an heir to the Dragon.
But heirs to the Dragon are thin on the ground these days, and I think we can safely expect that Daenerys Targaryen, who actually is the Prince That Was Promised (maybe), will legitimize him. Assuming he doesn’t stay dead, it’s just a matter of time.