An autograph in a dream (whether being given or being asked for) is usually indicative of recognition, fame, and desire. If you’re asking for someone’s autograph, you adore or respect this person, and would like to have some of the qualities that this person has. Maybe you’re asking your favorite author or movie star for their autograph, for instance, and this would indicate that you’d like some of the qualities of the author or movie star in question.
If, in your dream, you’re giving out autographs, it represents a desire or dream for you to be famous and recognised. You’re looking for applause and adulation, perhaps recognition for the work you’ve done. Unless you’re already famous and giving out autographs regularly, of course, in which case your dream is just a manifestation of your real life.