When exporting properties, only the internal values of groups can be exported. Since internal values cannot be changed, if you have changed the name of a group, the exported data will not match the actual group name.
Therefore, I propose the following, in order of priority:
Change "Group name" column to "Group Internal name" in the export file: This will prevent confusion for users.
Include the group name in the export file: This will provide users with the actual name of the group.
Allow users to set the internal value of a group when creating it: This will give users more control over the data.