Well, as far as I know the city was named Aren Deshar when LTT lived. He would've known its history then, as AS were well educated.

Aren Mador is a more recent name, dating to the days between the Breaking and the Trolloc Wars. My best guess is that Rand brushed up on his histories, and a place such as Far Madding had to have captured his attention (not to mention there was a time when he had good reason to learn more about the city).

Ah, I didn't realize it was called Aren Deshar during the Age of Legends.

"It's always been a city of importance, you know," Rand said from beside

Min , his eyes distant. "The Guardians are newer, but the city was here

long ago. Aren Deshar, Aren Mador, Far Madding. Always a thorn in our

side, Aren Deshar was. The enclave of the Incastar—those afraid of progress,

afraid of wonder. Turns out they had a right to be afraid. How I wish

I had listened to Gilgame . . ."

Perhaps this question isn't entirely simple, but...

Rand says:

"Calling me boy? I no longer mind, though it does feel odd. I was four

hundred years old on the day I died during the Age of Legends."

So his memories should be limited to those from the Age of Legends, correct?

Aren Deshar and Aren Mador are from way past the Breaking and the Age of Legends.

If he has memories of those cities that would make him well beyond 400 years old. He should only have past memories of the Age of Legends. How does he have memories/knowledge from cities 200 years past the Breaking? How would Rand know this?