Yes, they have names and they are… Drogon, Viserion and Rhaegal. In the last episode, we could watch the last two, the green dragons… but we are still waiting for the Drogon appearance because… well, we can use the web search and we are quite sure that he will appear soon.
According to the wikia of Game of Thrones:
Drogon is slightly larger than his siblings. Most of his scales are black, shadowing a red ones that run down his back and neck. His wings and frills are black-red mix, down to the wing-bones which are black. His eyes are orange red. Over the course of the series he has grown considerably, from being the size of a kitten in season 1 to the size of a large lion in season 4.
I must recognize it. This dragon, Drogon, is my favorite character on the series. He is like the rebel and I love these characters.
Drogon is the most aggressive dragon and, I figure, the smartest one.
The three dragons were born in the Dothraki Sea, when Khal Drogo, the husband of Daenerys, died. It was one of the best scenes on the series and we are quite sure that the dragons will be a very important part in the plot of Game of Thrones.
We don’t know the end of the books, of course, but we cannot imagine an Iron Throne without her and her dragons. Anyway, this throne belongs to her and we are sure she –and her dragons, of course- will fight to recover it.
Well, winter is coming. Have a nice day, dear friends.
Video: Don’t mess with Daenerys Stormborn of Targaryen. Speaking Valyrian. Season 3, episode 4.