The problem is there are other columns of data which have the table name in it. Your best bet is to go to the custom class and modify the table name from there. If you can't then I suggest cloning it and modifying the table name when you clone it.
If you must modify the SQL directly, which not recommeneded at all because of the issues you're already seeing, you must not only modify the ClassTableName property of the CMS_Class table but you must also modify the ClassXmlSchema property of the CMS_Class table.
After you do that, restart the site in IIS (recycle the app pool) and try to make a minor change to a field on your custom class. If it saves, you should be set, try to rebuild your index. If not, I'd suggest reverting your datbase changes and cloning the object instead.