Renown won't trigger when a creature deals combat damage to a planeswalker or another creature. It also won't trigger when a creature deals noncombat damage to a player.

If a creature with renown deals combat damage to its controller because that damage was redirected, renown will trigger.

If a renown ability triggers, but the creature leaves the battlefield before that ability resolves, the creature doesn't become renowned. Any ability that triggers "whenever a creature becomes renowned" won't trigger.