From the game's encyclopedia
Renown is much like Prestige, but shared by an entire Dynasty.
A Dynasty gains Renown for the following:
• The number of currently living members
• The number of Rulers
• The number of Spouses to other Rulers
Note that a Ruler will not generate Renown should they have any Liege of the same Dynasty.
As with Prestige, Renown also counts towards increasing your Level of Splendor.
Renown can be spent by the Dynasty Head in order to unlock Dynasty Legacies and influence the members of the Dynasty in various ways.
A Dynasty spread far and wide between several different Realms will generate more Renown than a Dynasty concentrated within a single Realm.
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Renown is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "Renown is much like Prestige, but shared by an entire Dynasty." Patch 1.20.1.2, from game/common/game_concepts/00_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/00_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.