Nero and the Narada come from the future. They are transported (I use the term loosely so as to not be confused with the technology) back in time through the singularity created by Spock using the red matter. Because he comes from the future, it is conceivable the Romulans have the history of Starfleet to the point of their departure from their timeline. It would be easy for them to see who the crew of the USS Kelvin was at the time of its destruction. Putting 2+2 together would place George Kirk as JTK's father.
Nero could have just as easily been listening in on the communication between the Kelvin and the shuttle craft carrying Winona Kirk and baby Kirk as they go through the JTK naming process. When JTK arrives on the scene after the destruction of Vulcan, it is not much of a mental leap for Nero to know who this young Starfleet officer is ... how many James Tiberius Kirks can there be in the universe? Nero is no dummy by any stretch of the imagination ... he's just a little emotionally compromised.