I made a post but I think the mods took it down so I'll put it here and if nobody notices then I'll just post it later. Jon is a legit Targaryen. First let me say that I really like Rhaegar in the books and one of the reasons I was so excited for the reveal was that it would prove that Rhaegar was not a rapist but a good man. When he was not mentioned at all in the scene (though now I understand it would have been super clunky to talk about him on your death bed when you had more pressing matters like saving your son) I got really scared that, to simplify for the show, they would just leave him as a rapist and move on. But then it hit me that Lyanna tells Ned the child's name. A name intentionally kept secret from the audience and from Bran despite the show revealing to the audience a few seconds later that the baby is in fact the new KINGINDANORF. This gives me hope that Jon Snow is actually a legitimate child of Rhaegar and Lyanna because the show is waiting to reveal Jon's true silly ass dragon name later on when his heritage will actually mean something to the story. At the moment knowing who his mother is, is just a fun fact. He is still a bastard but nobody cares what his heritage is, so revealing he is actually a legit heir for Westeros is a moot point because every is willing to see past his blood already. The only time being a Targaryen will be important is when riding a dragon becomes trendy. I don't think they would hide his name just so they can leave the audience in suspense for 6 more seconds. I believe that by hiding his name they have drawn attention to it and have thereby marked it as important and I do not believe that that important name is Snow. TL;DR the showrunners hid Jon's real name because he is a legitimate Targaryen.