Using the correct callsign for the ATC unit ensures that the ATCO is confident that the pilot understands the level of service that is being provided. This is really more important in the Tower, where in the most extreme cases pilots have been known to take off or land without clearance, under the impression that the unit is FISO or Air-Ground rather than ATC. ("xyz information" rather than "xyz tower").
In many circumstances, without the aid of telepathy, only the ground station knows what service is being provided before that initial call. So yes, when I call "Littleville, G-ABCD" it's important that the reply is clearly "G-ABCD, Littleville Tower" or "G-ABCD, Littleville Information". At my own home field, only some of the ATCOs are qualified to provide radar services, so "Bigtown, G-ABCD" will be met with "G-ABCD, Bigtown Approach" or "G-ABCD, Bigtown Radar", and that informs my request for a service. But there's no point in guessing on the initial call.