Relic Seeker — ruling 1

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.

Relic Seeker — ruling 2

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

Relic Seeker — ruling 3

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.

Relic Seeker : règles, fonctionnement et interactions (MTG)

Relic Seeker is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Renown 1 (When this creature deals combat damage to a player, if it isn't renowned, put a +1/+1 counter on it and it becomes renowned.) When this creature becomes renowned, you may search your library for an Equipment card, reveal it, put it into your hand, then shuffle.

How it works : Relic Seeker

Original English text — Wizards of the Coast / Scryfall

#1June 22, 2015· Wizards of the Coast
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.
No other card is named in this ruling.
#2June 22, 2015· Wizards of the Coast
If a creature with renown deals combat damage to its controller because that damage was redirected, renown will trigger.
No other card is named in this ruling.
#3June 22, 2015· Wizards of the Coast
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.
No other card is named in this ruling.