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Hey, i have seen many people on this forum and their application returned because of issue with birth certificate. They will return your application if u don't have name on it because they won't believe it's your birth certificate. If I would be at your place, I do two things

1. Send 10th grade certificate to them with cover letter and explain the situation why I am sending this document and don't forget to mention your client id, passport number, name and all important information. But by doing this I will still worried what if they won't accept my this document and return my application so what I will do, I send another complete package to Cic so if they accept my first application then I withdraw my 2nd application and if they return my first package then I will be still in safe side and fall
Under current CEC rule .

Good luck
 
There is one Sept person CC got charged even he did not have his name on birth certificate.
 
PR4CAN said:
Did someone get AOR when applicant name is missing on DOB certificate

I would say it all depends on the VO checking the documents to grant AOR.