Only the database itself is updated, not things based on the table, though. So you do have to modify your own code and forms, as well as any generated code, from tools like the RI Builder or GENDBC code.
Even worse, any views that are based on a renamed table won't work anymore. You can't even open them up in the View Designer to fix the problem. The solution is to use DBSetProp() to gather and store all the relevant properties, and then redefine the view. The big problem is, of course, knowing that you have views dependent on a renamed table.