Phone Etiquette for Calling (Me at) Your Library

I don't always answer the phone here,
but when I do, I'm the Etiquette Police.

Okay, here's how it works. You call the library.

Ring! Ring!
Me: Your Local Library! May I help you?
You: Hello. I have a question. Are you open on Saturdays?
Me: Yes, indeed. We are open from Insanely Stupid Hour to Another Silly Hour.
Etc.
You: Thank you. You were very helpful and not at all snide!
Me: You're welcome! It's so refreshing to talk to someone who knows what they want.
[Hang up.]

Not:

Ring! Ring!
Me: Your Local Library! May I help you?
You: How are you?
Me: ... uhhhh. [Thinks: Who is this? Do they know me?] Fine?

When "How are you?" is appropriate:

Ring! Ring!
Me: Your Local Library! May I help you?
You: Hello, I'm calling to ask ... Wait a minute! Is this Miss Marf?
Me: Yes, it is ...
You: This is [Insert name of child who used to come to my storytime 20 years ago and is now married with a kid]! How are you?
Me: Ohhhhhh, [name inserted while I desperately try to remember who it is]! So good to hear from you! I'm doing quite well. How are you?
You: I'm just great! I'm in law school now. I was calling to find out about your hours on Saturdays.

See the difference? In one case, it was someone who was just calling for information and was a stranger. In the other, it was someone who knew and remembered me (even if I could not immediately recall them - which happens all the time). But I get this "How are you?" gambit all the time. As much as I'd like to respond with some version of, "Excuse me, but who is this?" I realize that I am at a public service desk and while I might think correcting someone's phone etiquette constitutes a "public service," I bet my boss doesn't.

So, I'm telling you. Have a nice day!