Why are you nervous? Lets say you got ITA you need to submit payslips, T4, work experience letter, all of them have your company name as YY, right? Same as that of your work permit. Your employmer will get verification email they reply on the behalf of YY company, also the same email as on your experience letter. So everything is good. In case something arise in case you can get a letter saying that your employer own 2 companies but you work as per the job and responsibilities as per you experience letter. You are abiding by the rules.
