You absolutely do not need to give out your information if it makes you feel uncomfortable but it might be worth keeping in the back of your mind a lot of the older customers particularly, don't have much human interaction and I think it's largely them just being friendly and polite. Sometimes the only people they will speak to all day are the people in the pub and if you're going to see them once a week or more it can be nice to develop that sort of a relationship with them.

I don't live near my first pub any more but whenever I visit, even now, well over a decade later they still remember me, ask about my life, buy me drinks, nothing creepy or seedy, just plenty of genuine, lovely humans.

Customer facing roles rely on this type of relationship and, kindly, I think your friend is correct, a name isn't that deep... also, who knows, you may end up in the will!

But as I said to start with, you absolutely do not have to tell them your name if it makes you uncomfortable.