I don't know if this is a therapist thing... I think many people do this and sometime overdo it (in that case it can annoy me). Maybe the idea is to emphasize recognition of the individual? Make the conversation seem more personal?

The other similar thing that sometimes bothers me: if there is a longer email thread between two people and someone signs every single message with their name, as though it would be unclear whom it comes from. This I have definitely seen overdone by both of my therapists.