Emergency contacts are contacts that are important in an emergency, to which SOS messages are sent or to which calls can be made even if the Samsung device is locked.

The emergency contacts can be managed in the Contacts app.

Android 10 (One UI 2.0)
Step 1:  Open the  Contacts -App
Step 2:  Tap on your own  profile
Step 3:  Tap on  Emergency contacts
Step 4:  Tap on  Edit
Step 5:  Tap on  Add member
Step 6:  Select desired  contacts
Step 7:  Confirm with  Done
Step 8:  Tap on  Save
  1. Open the Contacts-App
  2. Tap on your own profile
  3. Tap on Emergency contacts
  4. Tap on Edit
  5. Tap on Add member
  6. Select desired contacts
  7. Confirm with Done
  8. Tap on Save

Samsung Instructions