Most code list names cannot be renamed in the CRM (Status, Relationship, Source, Owner). The exceptions are the Category and Classification code lists, whose names you can edit as needed.
You will find these code lists for all types of records and they may have different names for each.
Only the administrator can change the names.
First you need to turn on the rename option in Settings -> Extensions -> Rename fields
Then click on the Category name (it is underlined) in any record.
Enter a new name and confirm with the Change button.