Hi Sunny, 

There is no denying the fact that it is difficult to  make changes in school certificate, so the smart move would be is to apply using the name written in the school certificate. You can change the name wrriten in the aadhar card later.

You should go with the name printed in the Aadhar card. It is what will matter for ID sake and thus, you should fill the name in Aadhar card and not the school certificate.