Not exhaustive, I even intentionally skipped characters that are so far removed from relevance. But yeah, you forget how big the Main Gen is, since Marauders Gen seems to have overtaken it in popularity and it's side characters get fleshed out more (which feels odd since even relevant main characters don't have that many fans). Like damn, Main Gen really has this many characters. This Era contains people born c. 1965-1985. So from the HPHM prefects (Angelica, Jane, Chester and Felix) to Grim Fawley and Emma Vanity II.
Generic Names To Use For The HP Games MC's (For The Sake Of Having a Character Without Feeling Self-Insert-y):
(Providing it as Feminine/Masculine/Neutral Surname, you decide what gender you want to give the character. I have also put the games in chronological order.)
Hogwarts Legacy (1880): Main Character = Mary/Marcus/Mars Charbonneau ("Star of the sea"/"Of Mars"/"God of War" "Charcoal - often in reference to dark skin")
Hogwarts Mystery (1983): Jacob's Sibling = Sybill/Shib/Sybb Chambers ("Prophetess"/"Kind"/"Prophet" "Servant working in the Lord's chambers")
Cases From The Wizarding World (Early 2000s): Mathilda Grimblehawk's Partner = Parsley/Parker/Paris Khimaira ("Fragrant herb"/"Keeper of the park"/"Warrior" "Monster made of many beasts")
Magic Awakened (2008): Main Character = Maisie/Mason/Mace Charelston ("Pearl"/"One who works with stone"/"Blunt weapon" "Settlement of free men")
Wizards Unite (2016): The Calamity Investigator = Calypso/Callum/Calli Innsmouth ("To conceal"/"Dove"/"Beautiful" "Rest at the mouth of a river") (Since this character is around the same age as the main gang I did also give them the daughter Amity Innsmouth, you may or may not use this character as part of the Next Gen but she's not canon.)