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Source: AccountContactRole

This object defines a role that a given Contact plays on an Account’s opportunity.

There could be only a Primary Contact for every Account.

Add the Contact Roles related list on the Account object.

Click on New, and select a Contact from the CRM, a Role from the picklist and whether he is Primary or not for the Account:

If you select the Primary for another Contact, it will be elected as Primary contact and the other one will be flagged to false.