From the game's encyclopedia
A Bastard may be Legitimized, either at birth, or as a Character Interaction later, depending on approval from their House Head.
A Legitimized Bastard has the same right of inheritance as Legitimate children, but the stain of bastardy will follow them throughout their life.
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.
Legitimized Bastard is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Bastard may be Legitimized, either at birth, or as a Character Interaction later, depending on approval from their House Head." It is part of Bastard. The game also links it as Legitimized. 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.