All our teams are COBRAS and that is what we all go by first and foremost. But last year we decided to give all our team fun names instead of calling each team by their level or some hierarchy of elite, national, advanced etc. We decided to choose things that everybody liked and that didn't have any connotations of one thing being better than another. Last year we were colours, and this year we are Jelly Belly Flavours - next year, who knows: cars, Pokeman, elements on the periodic table? We like it cause it allows each team to build a personality around their flavour. We make up cheers, slogans, have t-shirts made and generally get really into it.
As coaches it allows us to put athletes of like abilities together at the start of the season without having to determine their competition level before they've even worked together. Each team will be the level that their team becomes - the sky is the limit for them if they wish to put the work in. We determine levels for each team around choreography and even then it may change throughout the year. So calling "Mango" Mango is better and less limiting for the team than calling them Level 2, because they just may be a Level 3 team by the end of the season.
We switch it up every year because 1. its fun and 2. it avoids us creating any hierarchies ourselves and 3. it allows us to have a contest every March or so and give away prizes to the person that comes up with next year's concept.
Don't hesitate to contact me if you have any questions.