Data must be a pretty big celebrity in the Federation, he's got to have a lot of recognition.
Besides Picard and Data, there are probably more people who know of them than know what they look like. Worf must be famous among Klingons and somewhat well known on Earth. People are naturally going to give Picard credit for most of the ship's accomplishments. And while their adventures may be exciting when watching them, I can bet the actual mission reports are dry and wordy, so they aren't heavily reported on.
Before the Dominion War:
Federation News Service Page 1: "80 degrees and sunny in the beautiful clean air of Los Angeles. Denobulan pop singer Rhavix tours Andor, divorces Vulcan wife?"
Federation News Service Page 80: "Enterprise D escapes ancient booby trap, left by ancient extinct dynasty".