Let's call something a rigid designator if in every possible world it designates the same object, a non-rigid or accidental designator if that is not the case. Of course we don't require that the objects exist in all possible worlds. . . . When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed. A rigid designator of a necessary existent can be called strongly rigid.
My dad had a church of 90 people when I was born. It was just, over the years it continued to grow.