The dream about the show that is called David Letterman show, means that you are the person who like to socialize with others a lot. Some people who watch a lot of television dream about the previous shows they saw before they went to bed. In this case the dream means nothing, it simply shows the reflection of your waking life.
Dream dictionary: david letterman dream meanings
To dream you are on a talk show or that you are friends with a talk show host can mean that your subconscious mind considers that person a friend because you “interact” with them often, or like to “interact” with them by watching their show. (The subconscious mind doesn’t see much difference between a person talking to you from the TV and a person talking to you in person.)…