Alarm only available once per day

I think you are using the wrong alarm function.

There is an alarm function which is linked to the Health app, which tracks sleep and helps with a better sleep rhythm. It is the one called Sleep / Wake Up inside the Clock app. You should NOT use it for a quick nap.

To set an alarm:

1. Open Clock app

2. Tap "Alarm" at the bottom menu.

3. Tap "+" in the upper right corner

4. Set the Alarm to the desired time and tap Save.

You can add as many alarms as you want, and activate and deactivate the ones you want to be active.

You can find more useful information here:

How to set and change alarms on your iPhone - Apple Support

Open the Clock app, tap Alarm at the bottom of the screen, tap the + sign at the top right of the screen, set the time for the alarm today and tap Save at the top right of the screen.

You're welcome.