The identity comes from the coach IMO. It's his philosophy that trickles down through the team and onto the court.
Again, this team improved too quickly which allowed BC to deviate from the traditional method of re-building. The division title and Sam's COTY award have proven detrimental and exposed Colangelo as a reactionary GM instead of a "stay-the course" long term thinker.
A return to tried and true re-building practices, starting with the hiring of a skilled and single-minded head coach, is ultimately what will help establish not only an identity but a tradition of winning basketball.