I'm thinking that Robb's legitimization is a legal document specifically saying something like "Jon Snow, the bastard of Eddard Stark, will now be known as Jon Stark, son and heir to Winterfell and all her holdings..." etc. So no, I don't think there's some kind of blanket legitimization that would allow Jon to take the Targ name instead of the Stark name (if he is in fact the bastard of Lyanna and Rhaegar). In fact the only consequence of the discovery that L+R=J would be that Robb's legitimization of Jon would be nullified since the "Bastard of Eddard Stark" part would no longer be true. Of course the sticky situation you bring up could still happen if Jon is actually the trueborn son of a married Rhaegar and Lyanna. I'd prefer a rivalry/uneasy alliance between Dany and Jon to the kind of sappy love story Jon Blackfyre proposes :stillsick: so it's an interesting idea.