There is actually a name for each team:
Umeshu -UME/LIQUOR- (Ume from Umeko, Shu from Sakai's first kanji
http://en.wikipedia.org/wiki/Umeshu)
04. あこがれアイドレイション / 梅酒 -UME/LIQUOR- [12,14]
KANI SEVEN (tiresome/troublesome members or 面倒くさいメンバー. I don't know the exact meaning. I wonder why Sekimayu in this team.)
05. カニ子 / カニSEVEN [12,13,17,22,26,30,32]
B-gataΩIdoling!!! (blood type B )
06. 戦闘恋愛少女ロボB型の憂鬱 / B型Ωアイドリング!!! [13,15,16,25,26]
U-17ing!!!
07. Bon Voyage! / U-17ing!!! [17,22,27,28,29,30,31,33,34,35]
PEACE!Idoling!!! (unknown)
09. 夏のお嬢さん / PEACE!アイドリング!!! [3,6,9,12,13,14,15,16,17,19,20,26]
Nakimushi Idoling!!! (the crybaby)
10. 涙のフリージア / 泣き虫!?アイドリング!!! [15,16,20,29]
Idoling NEO
12. プリ▼きゅんサバイバル(※▼はハートマーク) / アイドリングNEO [23,25,31,32,33,34,35]
Shittori♮Idoling!!! (obviously members with better singing skill. surprisingly no Kaoru.)
14. Promise / しっとり□アイドリング!!!(※□音楽記号のナチュラル) [3,6,9,17,19,23,31,32]