First, a primer: buon giorno is "good day" or "good morning"; buona giornata is "have a good day," or "have a good one," or "have a nice day." I can remember, or think I can, when clerks in the US started saying "have a nice day." I thought then it was cloying and artificial and excessive, and though I've grown used to the phrase, it still grates on me. I can't speak for Dianne, but I do know that she doesn't use "have a good day" in the States but has recently taken to using "buona giornata" in Rome, and merchants seem to respond well to it.
The coffee cup combo in the photo, provided the bar by a major Rome milk distributor, takes "buona giornata" to a new level--indeed, takes possession of the phrase and offers it back: "Sponsor Ufficiale della BUONA GIORNATA: Official sponsor of 'have a nice day.'" All, I hope, with a sense of irony--but even then I don't like it.