Hitchhikers cannot call Shotgun. They should be happy just to have a ride, and calling Shotgun in this situation is disrespectful.
With this being said, there are scenarios in which you might prefer for your new companion sit up front. If said companion looks like the mangy, stabbin’ kind of hitchhiker (Why did you pick them up in the first place?), you’re better off with him riding Shotgun so that he cannot jump you from behind the driver’s seat. Conversely, if he is the enlightened, peripatetic-wanderer kind of hitchhiker, he might offer you some type of gift or enlightenment for picking him up and you might honor him by inviting him to ride Shotgun.