"Thank you, Jonathan..."
The use of my first name always catches me off guard when a server or cashier hands back my credit card with the receipt. I invariably go through a mental checklist: Do I know this person? Have i been unintentionally snubbing him or her? If I know my server, when and where did we meet? If I still can't place the person, I assume we're strangers and have only been acquaintances since I've been inside the restaurant.
It could be in the inflection of the server's voice or my mood, but at times I find it infuriating -- like someone is taking a liberty. But whether this is disrespectful or just a sign of friendliness is what is open to interpretation.
A server only goes by his or her first name, so it's not that formal an interaction. I've been at tables where another diner will make a joke by introducing everyone at the table by their first names in response to the server's greeting; I'm sure the waiter wasn't amused. So, it's safe to say there are trangressions on both sides of the napkin.
But I have a last name and it's right there on the credit card receipt. That means the server has four options at the end of the meal. The first is omission: My name doesn't have to be mentioned, which is perfectly fine. Or a server can use either my last or first name, with the latter likely being the right option. The fourth is the most awkward: the use of both my first and last names, a la the girl alien from the remake of Race to Witch Mountain. This is perhaps only acceptable in robot or science fiction-themed restaurants.
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I really, really dislike the ubiquitous "My name is Scott and I'll be taking care of you today." Strangely, it seems to make the interaction more formal than it needs to be.
Proper server etiquette is not using the guests name until they have introduced themselves to the server and asked for your name. Then a server can greet them by first or last name depending on the business to casual style of the meal. This is also a great way establish a guest to come back and ask for the server by name. A win/win for both the server and the restaurant.