I sympathize with your issues; we have the same ones. There are bugs in the rename function which support is looking into. If you haven't already please try to work with support to help the community solve the problem.
As far as machine identification, we use the Agent tab and customize the Agent Status page to include Last Logged in User, Current User andComputerName (not to be confused with Machine Name). That's pretty much all of the information you'd need to identify the person from a helpdesk perspective.
We're doing this on nearly 5,000 endpoints so I completely understand your situation.