I think the history of the name is similar to PUBG. The original games name was Pocket Monsters, but the community just abbreviated it to “Pokemon”, because Pocket Monsters isn’t a word they can pronounce correctly. But it wasn’t the part of the name at all. You can check the game title, cartridge image and packaging. In a later international release because of the trademark issues they just used the shorter name instead.

I think to this day the games are named “Pocket Monsters” in Japan, but with “Pokemon” added in front. But I’m actually not sure about this. One source to look for are game box-art covers: pokemondungeon.com/media-downloads/box-art and on archives.bulbagarden.net/…/Category:Game_covers

• Pokemon Blue (Game Boy, Japanese)
• Pokemon Ruby (Game Boy Advance, Japanese)
• Pokemon Sun (Nintendo 3DS, Japanese)

But in newer games (I don’t know since when) they seem to have dropped the “Pocket Monsters” part from the actual game name entirely:

• Pokemon Legends Arceus (Switch, Japanese)