“How soon can you fit me in?” was not treated as a question about your diary. Neither were “what is the earliest you can do”, “when could I get in” or “when is the soonest”. Your receptionist did not look at real availability for any of them, so the answer was not grounded in your timetable. That is the caller in a hurry — a broken boiler, an interview tomorrow — and the one you least want fumbled. It now reads out your genuine next free appointments.
“Can I rearrange?” reached nobody. If a caller said “is it possible to rearrange my haircut” rather than using the word “appointment”, nothing recognised it as a request to move an existing booking. It is now passed to your team along with the caller’s contact details, the same as a cancellation. Your receptionist still never moves or cancels a booking itself.
Asking to change the day part-way through booking is unaffected — that is an ordinary part of choosing a time, and it still is.