The Sender Is Listed As A Four Or Five Digit Number

This is an internal number to your mobile telephone carrier. In the U.S., there is no way of having a message display your name unless the message is coming from a phone number that has your name inside its phonebook. There is also no way of faking a message to make it seem like it's coming from your phone number - if there were such a way it would be a huge security risk - anybody would be able to send messages to any phone using your phone number. This is the way that mass text messaging works across all carriers at  the moment.