Proper names are standardly claimed to be rigid designators i.e. to refer to the same objects with respect to all possible worlds. Apparently, this view is incompatible with the assumption that statements such as “The object o need not be named α” or “The object o might be named β” (where it is true that α is the proper name of o) are true. The reason is that the naming relation is merely contingent. As a result, one should make room for the possible worlds with respect to which the naming relation does not hold. The aim of the present paper is to show that this line of argument fails because it ignores certain vital distinctions making the above mentioned statements ambiguous. The problem is eliminated once linguistic expressions are strictly distinguished from semi-expressions and the real world is distinguished from the actual world (and other possible worlds).