Hi Rogier,
To remove their access you need to change the permissions on each profile field. You can do this from Admin->Directory->Profile Fields. From there, select the field you want to edit ,and go to "Edit Field":
Name - General
Location - Location
From there, you can go to the Field Permissions tab, and under "Writeable By" change it to Specified users. Then you can control what users roles have access to change it.
You can do this to lock down every profile field, if you wish.