When you become a Buddhist, it doesn’t involve joining a group or becoming part of a “people”.
For example, when you convert to Judaism you become part of the Jewish people. When you become a Christian you are part of the body of Christ. Many Christians believe that God works specifically through the group.
In Buddhism, conversion is really a personal matter and there is no need to join a group. In traditional Buddhist countries people don’t think of themselves as members of the local temple. They have a relationship with the temple, but it is as a supporter and participant. In western countries, Buddhist temples or groups usually maintain a membership to meet legal requirements.
When a Buddhist becomes a fully ordained monastic then they become part of a group known as the Sangha. This involves an official procedure that requires members of the Sangha accepting you into the group.