I think there may be a slight problem with calling these "Premier Events" -- I don't know what the system is where you are, but at least in my area "Premier Events" is a term already used to refer to the more formal events which award points and have a more expensive entry fee (such as League Cups and Challenges), as opposed to your ordinary Leagues and larger Tournament Events... Although I can't say I have a better suggestion.I thought about it for a while, looked at a bunch of synonyms to "easy", "single", "basic", etc. and stumbled upon "Prime". It has correlation to "one", as in the number of prizes, and "primeval", as in basic. The absolute best derivative I found is:
This one gets even better with a direct correlation to a Pokeball. It also just sounds like a format name - "Standard, Expanded, Premier". Let me know if this one sounds good to you.
This naming convention comes straight from the Pokemon Event Locator btw, which I've linked.