The Teacher role does not contain permission
to change the course category, so if your teachers are able to do it, they are getting the permission from elsewhere. However you raise a legitimate issue with the names.
The Teacher role has moodle/course:update ("Update course settings") = Allow. This allows them to change all of the other settings on the Edit course settings page, including the course name and short name. So currently, it's all or nothing. I think there's a strong use for providing a separate capability for the course name and short name, say moodle/course:updatecoursename.
When a course is created by an administrator or course creator, they must enter the category, name and short name. In fact, these are the only required settings. This implies that the names (like the category) are the concern of the creator, not the teacher, and the teacher should normally be prevented from changing them (i.e., the Teacher role should have moodle/course:updatecoursename = Not set).
I just created MDL-15262
"Teacher should normally be prevented from changing the course name and short name" and referenced this discussion.