I disconnected TSheets from my client's QBO via the App screen on QBOA. Then the client was able to connect their own TSheets account.

No one has selected the wrong company name.   So I do not understand that part of your answer.

The TSheets connection occurred when I was using my TSheets account/connected to my QBOA to record time I worked on that client's work.  

How can my QBOA be connected to my TSHeets account and used to track my time working for my clients--but not show that it is connected to my client's QBO account?  Is there a setting that needs to change?

That is the question.