Yes, such an excellent point. The Holy Orthodox Churches are united in communion and doctrine. The petition of the Divine Liturgy "..for the good estate of the Holy Churches of God, and unity of them, let us pray to the Lord," is one of our prayers so that all Orthodox Christians pray for the the unity of the church, the One Church.
In addition to manifesting our unity through the chalice, I always look to the Bishop's Throne, which reminds all Orthodox Christians that they are not "independent" parishes, but "dependent" parishes, dependent on the authority of our bishop. Throughout the world, Orthodox Christians pray "First of all, remember our Bishop...," who, commemorates the head of the provincial synod of which he is a member, and the "First among them," the primate of a region, commemorates the primate of the Holy Synod which governs his province; (not there there is necessarily a province), in which case the diocesan bishop commemorates the primate of the Holy Synod of which he is a member. And finally, the primates of the Holy Churches, commemorate each other, all the primates or heads ("celfaly," in Greek) of the Holy Orthodox Churches, a wonderful witness of the unity of the Holy Orthodox Church.
For those who don't know, "autocephalos" means "self-headed," simply having the privilege or right of electing the head of the local church, without reference to another of the sister Orthodox Churches, such as in regard to an "autonomous" church which must have the election of its primate, or first hierarch, approved by the mother church to which it refers, or is under.