As Barry mentioned, Game ID/Name association shouldn’t change, but there is some rare cases which are worth noting in case it may impact your app.
For example, one thing I’ve run into is with WoW and how they cycle expansions. For example, when Battle for Azeroth went into beta, that was added to the games list, and Legion removed, same as has happened with previous expansions. So if you used the games endpoint and looked up a game by name, for ‘World of Warcraft: Battle for Azeroth’ you’ll get specifically that, but if you set the name to ‘World of Warcraft: Warlords of Draenor’ or ‘World of Warcraft: Cataclysm’ they’ll return the original ‘World of Warcraft’, including the original game ID.