TV dramatics. Just like in Yesterday's Enterprise, when Tasha reads off the ID on the other ship. "NCC 1701-C, U.S.S. ...Enterprise." But Picard doesn't act stunned until she gets to the Enterprise part.
Actually his stunned reaction (Riker's too) is after Yar reads off "1701-C". He turns to her, and then after she reads "Enterprise", he looks back toward the viewscreen.