Whereas on older Samsung devices the alarm tone could only be changed for the alarm clock in general, nowadays we can change the tone for each individual alarm clock, and in addition to the many standard tones, a separate alarm tone can be added.

Android 10 (One UI 2.0)
Step 1:  Open the  Clock -App
Step 2:  Tap on desired  Alarm
Step 3:  Tap on  Alarm sound
Step 4:  Tap on  Ringtone
Step 5:  Choose desired  Ringtone
Step 6:  Tap on  Back
Step 7:  Tap on  Back
Step 8:  Confirm with  Save
  1. Open the Clock-App
  2. Tap on desired Alarm
  3. Tap on Alarm sound
  4. Tap on Ringtone
  5. Choose desired Ringtone
  6. Tap on Back
  7. Tap on Back
  8. Confirm with Save

Samsung Instructions