Warning!! The post has a lot of GOT spoilers!!
In a not so shocking reveal in the season finale of Game of Thrones, Jon Snows true parentage was officially revealed, since he was born on a Dornish island in the Tower of Joy, he ought to be named Jon Sand, but he was not truly a bastard since Rhaegar actually married his mother Lyanna, leading Bran to make the statement "Roberts Rebellion was based on a lie". Perhaps if Robert realized his betrothed Lyanna fell in love with Rhaegar the rebellion would never have begun, but with the way the Mad King was going, he would have probably still lost the throne anyway, but this time it would likely have gone to Rhaegar.
So what is Jon Snows real name, it's not Jon, since that was the name given to him by Eddard, naming him after Jon Arryn, to cover his real name which was obviously a common Targaryen name, and it's not Sand or Snow seeing as though he's not a bastard.
As the new three eyed Raven heard with his own ears, Lyanna named her son "Aegon Targaryen"
It would be worthy to note that Rhaegars first son with Elia Martell was also named Aegon and it's believed He named both his sons Aegon in line with the prophecy and his belief that the Dragon has three heads, however his first son with Elia was murdered by the Mountain alongside his sister and Mother, but some believe he survived this ordeal and is currently with Jon Cunningham and the Golden company as Young Gryff, but that's another story entirely.
There have been approximately 11 people or thereabout named Aegon in the Targeryen family, but only Kings get a numeral added to their names, so if Jon Snow becomes the King of westeros he would be, Aegon VI Targaryen, being the 6th King to bear the name.