It is usually named after the player/players who first played it/devised it/popularised it Eg. Ruy Lopez, Najdorf, Richter-Rauzer, Nimzo-Indian, Reti opening, Botvinnik system etc. Either that or the place it was first played/came to attention Eg. Cambridge Springs variation, Archangelsk, Gothemburg variation.
Opening names
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Probably just becomes accepted through regular use. Or if a top player refers to it. Or if it appears as such in chess publications etc. There is no grand council of name givers.
Chessplayers en masse. No one in particular. Whatever obtains popular usage and gets repeated most often, especially in print. As said above, it is usually named after a place it was first used a lot, or after a strong player who played it a lot. Not necessarily the player who invented it.
Who determines the name for openings? How does it ckme to be what it is called?not everyone has the luxury of giving certain moves names, so who is doing it?