Question : Problem: If I change computer name will SMS update correctly

We have computers (desktops, laptops, workstations) that may remain with the user as they move through different business units. We will change the WS ID (workstation name) to represent this. I know that AD and DNS will update.

We also have SMS in out environment. Will SMS be updated as well, or is that a manual job?

Answer : Problem: If I change computer name will SMS update correctly

This depends on what SP level you have. By design, it should retain the HW inventory of old name and create a new inventory of the new name in the SMS database. You may want to check on the SP level and patch here http://support.microsoft.com/kb/903933

Also, on your site maintenance configuration, you have have configured to delete aged info. If that's the case the old name will disappeared eventually. If you configured your discovery method to scan from the AD system, you would have a clean and closest info on both SMS and AD.