Game of Thrones: We have to change Asha’s name to Yara because people might confuse her with Osha.
Game of Thrones: We have to change Robert Arryn to Robin Arryn because people might get him confused with Robert Baratheon.
Game of Thrones: Uh… Rhaegar named both his sons Aegon.
Okay, so Jon’s father was a Targaryen, but his mother was a Stark, Ned, his de-facto father, was a Stark as well, Jon looks and acts like a Stark, its the biggest part of his identity. Being a son of Rhaegar doesn’t change who he is.