What makes a prince renown?

There are a few ideas here. Renown basically comes down to respect. Conquering other lands is always a good thing. Keeping things running smoothly in your own land is good. If neighbours are fighting, pick a side and obliterate the other; you will look like a real "kick-ass" leader. If you don't pick a side, you will look weak and the winner of the neighbouring conflict may come after you.