Just starting off here, only playing core set:

I attack into the Baratheon player and he defends with Robert Baratheon Core. He wins the challenge.

Does he gain renown or is that only when Robert is chosen as an attacker?

Thanks!

Zimagic

Renown works on both defense and offense. So if you defend and win the challenge, any character with renown you control that is in the challenge gains a power.

Ok, thanks! I thought it was just on attack, but apparently not!

When in doubt, check the rules

Renown

If you win a challenge (either as attacker or
defender), each of your participating characters
with the “Renown” keyword claims 1 power
after the challenge resolves.