If we're willing to accept that a Dragonborn was born to conveniantly coincide with the return of the dragons in the first place I don't think it's unreasonable to assume that those same forces would bring Alduin and Dovahkiin together.
The first dragon definatly knew you were Dragonborn before you defeated it. If you fight it with subtitles enabled the shouts/roars are translated to "Dovahkiin, No!" when you hurt it. So if that first dragon knew you by sight, Alduin must have aswell.Agayek said:Most likely because nobody knew the PC was Dovahkiin until that first dragon kill. At the time, he was some random schmuck. Alduin choosing then to attack was just a random stroke of luck/irony.