The idea that Dany would obviously know who Tyrion Lannister is because of her family history is stupid. This is a girl who only recently learned the truth of her own father from Ser Barristan, and who was only just learning about her own brother from the same guy - after a couple of years in the presence of Westerosi people, too. She has been sheltered from a lot of this stuff. While she would know that the Lannisters killed her father and hold King's Landing, there's every chance that she wouldn't know Jaime's brother, or the fact that he's a dwarf. She has been completely divorced from Westeros, relying on second-hand info which has tended to be only the most relevant things. The identity of Tyrion Lannister has probably never come up.