Here I would like to know more about name mismatch in your particular case. I mean, do your all certificates have same name or there is a variation? Because if it is not same in all the required academic documents, you first need to get them corrected.
For this, you can go for affidavit from the court/ advocate of your own place.
You have not mentioned about the types of mistake. I mean it is just a minor spelling mistake or a remarkable change in name?
If it minor, it may get considered by the document verification panel.
Name mismatch in documents becomes more problematic when you wants to apply for government jobs and for abroad jobs. So it is always advisable to correct the mistake at the earliest.
If you do not want to get it corrected at this point of time, do mention the name which is mentioned on your certificates.