You cannot build a team merely by replacing “me” for “we” in communication. You won’t get there either by placing people in one room and giving them a common name. A team is much more than a group of individuals sharing the same space and some characteristics. What binds a team is spirit, not labels.
A leader’s role in team building is defining and distributing work in such a way, that naturally requires team cooperation to achieve goals. Ideally, failure to cooperate should result in failure of the whole team. Remember the movie “300“? Leonidas explains to the deformed Ephialtes how Spartans fight: as a single, impenetrable unit. Arm to arm, fighting the same enemy, protecting each other. That is team spirit.