Yes, you can set a label of your choosing in a court slot. When a slot is booked for any reason the schedule will show details of the booking as appropriate. But if unbooked, the default text is either "Available" or "Unavailable" depending on the members ability or rights to that slot. However, you can choose to change this for certain slots.
Suppose you wanted to annotate your peak slots as "Peak" and your off-peak slots as "Off peak". Simply create a court set in the Court sets tab of Manage courts (you probably have these set up already) and edit the details of the court set - in the popup window you'll see an opportunity to set a label. Type in "Peak" or "Off peak" as appropriate and the job is done.
You can set a label on any court set. Should the same slot be represented in multiple court sets with a label, then the schedule display will simply show all of the labels separated with a "/" character.