Teams never have names. They are given numbers just like in the Show. If there is a jounin or chuunin in team then the team will take on "(jounin/chuunin name)'s Team". That is how the current Team system is.
acualy in show the still used squads with jounin eve when the genin became huuninlike with naruto and sakura nd naruto,sakura, and i thinkhis name is aoi as the rplacement in manga , also in kakashi gaiden special it showedthe squad and kakshi first being jounin meaning he was alreay a chuunin so is squadmembers had still been together.
