Designated post offices have a service called ______ available for transients?

The correct choice is "General delivery." This service is specifically designed for individuals who do not have a permanent address, allowing them to receive mail at a designated post office. General delivery can be particularly useful for transients, travelers, or those in transition between residences, providing a reliable means of receiving important correspondence without the need for a permanent address.

Services like Priority delivery and Express services focus on the speed of mail delivery rather than the accommodation for individuals without fixed addresses. Meanwhile, a Temporary hold refers to a different service where mail is held at a customer's request when they cannot receive it at their address, rather than being specifically geared towards transient individuals. Thus, General delivery is uniquely suited to meet the needs of transients, making it the correct answer.