Not sure if it's been mentioned in the books or the show, but what happens if a bastard marries a woman of a noble house?
Let's take something random, like Jon marrying Dany. Would he legally become a Targaryen, or would he still keep his surname?
Imagine if he was legally a Targ all along. If R really did knock up L and they were in love, them being married in secret isn't far fetched. Aegon the Conqueror had two sister wives after all.