Calendar does not have an option to mark a time as busy or booked, except as noted below. If you think this might be useful you can send Apple some feedback here (this is a user forum and Apple doesn't read the contents).
There is one circumstance where it might have this capability. The User Guide says
If you see Check Availability below the last invitee, you can click it to see when invitees are free or busy. You only see Check Availability if your event is on a calendar service that tracks availability, such as CalDAV.
You see invitees’ free and busy time in the Availability window. To find an event time with the fewest or no conflicts, you can:
- Move the event: Drag the event block.
- See another day: Click the arrows at the top of the window.
- See the next time all invitees are available: Click Next Available Time.
An option therefore is to acquire a third-party calendar and two are often mentioned in the Apple tech websites. I don't have or use either so I can't advise about their suitability for your needs.
Fantastical (user guide here) and BusyCal (user guide here) are both available in the Mac App store. Both seem to have options for marking times or events as booked, plus many other features often used in a business setting.
Other calendar software can be found in the App store but I have no insight about how they function. I always meant to have a look at these two but, like many Mac users, the basic Calendars app does what I need and I had no motivation to find alternatives with, perhaps, extra or more sophisticated functionality.
