I read Daenerys chapter where Rhaegar was mentioned and then came Jon's chapter, that made me thinking. I always doubted that Jon was Ned's son, too much honor to do that I guess and he never talked about his mother. Then I remembered how Rhaegar kidnapped Lyanna, they both died during the rebellion and Ned comes home with a baby.
"Dragon has three heads."
Danny and Jon make for two I guess, really wonder who's third.
Even if he is a child of Rhaegar and Lyanne I wouldn't call him Targaryen, much more Stark traits, dark hair, warg, fire can hurt him...
Raised a Stark and with their colorings but still the name follows the fathers side.
You may have also noticed that at the Tower of Joy there were kingsguard but there was no king there.. if Lylanna and him weren't married then there is no reason for them to guard her... Lylanna's bed had blue flowers, and in Dany's prophecy in the house of the undying showed a blue rose growing in the crack under or in The Wall.
This isn't exactly how they show Ramsay in the books, by the time we get to Theon all this has happened. I'm fairly certain that I remember Theon thinking about an event just like this where he had helped him escape only to catch him and bring him back to the dreadfort.