Bran might see it's best to keep it secret, also. The truth would give Sansa the north, who is not trustworthy, not only did she keep her alliance/dealings with the Vale secret TWICE, she looks completly unhappy at Jon's rise as King, and it has given LF a big opening. Bran has the responsibility as the Three Eyed Raven now, who was known to keep secrets and even lie (like Bran's ability to change the past), because of the consequences the truth could bring. Telling Jon's secret would not only throw the north into chaos, as he would no longer be king of the north, but it would put Jon right into Dany's cross hairs, as he would have a better claim (birth right) to the iron throne than she does.
Jon also just makes the most sense in marriage for Dany. They need the north, winter is here, there's a good chance Euron is lying in wait with a thousand ships to undercut her. They still have the Lannisters to worry about, the Vale and the chaos that is house Bolton. Also, the north is the only protection they have sans dragons to prevent extermination from the Night King. Dany is going there to marry a leader/king of one of the realms to unite Westeros, as she stated in the last episode. It's either Jon, king of the north, Littlefinger, Sweet Robin, or Euron. Who do you think she'll choose?
Jon has already united the north, people follow him, he's a natural leader with a great reputation. Tyrion knows Jon and his honor, and he knows the treachery of the other houses. Jon needs men, especially if the Vale turns on him, which they no doubt will. A Jon and Dany marriage makes the most sense. Dany will want to marry him, she'll be advised to, not only for strategery, but having the north and south gives her ultimate power. And she would WANT to marry Targaryan blood, anyway. If you could construct a perfect husband for her it would be Jon.