Since Rose and "Ten Too", the half-Timelord/half-human Doctor, are in the parallel universe for presumably the rest of their lives, is it logical to assume the Doctor would tell Rose what his real name is? Has there ever been any mention or evidence that points to this? I'm wondering if Rose is actually part of the small group of beings who know the Doctor's real name.
Canonically, we know absolutely nothing about Rose and Ten Too after they're left standing at Dårlig Ulv Stranden in the other universe. The real Rose Tyler appears only once more--when the Tenth Doctor is making his farewell tour, his last stop is Christmas the year before Nine met Rose, where he briefly interacts with her regardless of the possible paradox. After that, we see the image of her, chosen by The Moment as a user interface despite being out of sequence for the War Doctor. As far as we know, the Doctor has has no further contact or interaction with that parallel universe, and we have not been shown any, "Meanwhile, in Pete's World" moments.