You can change the name of self-created contact groups at any time in the app, but you cannot rename standard groups such as family, colleagues or friends.

Android 10 (One UI 2.0)
Step 1:  Open the  Contacts -App
Step 2:  Open the  menu
Step 3:  Tap on  Groups
Step 4:  Tap on desired  Group
Step 5:  Tap on  Edit
Step 6:  Tap on  Group name
Step 7:  Confirm with  Save
  1. Open the Contacts-App
  2. Open the menu
  3. Tap on Groups
  4. Tap on desired Group
  5. Tap on Edit
  6. Tap on Group name
  7. Confirm with Save

Samsung Instructions