Different name on passport and academic documents

My name in my academic documents is mehak kxxx.

My passport has the name of mehak kaur taneja.

So I want to study in US I have already given my gre and ielts with the name of mexxx kaxx taxxxx.

So, my given name in all my documents is same but my passport ,gre and ielts have my surname also.

Will it be a problem in applying to US universities or if I get a Affidavit will that work?

It should be fine. The key thing is that your passport and GRE docs should be same. One of the things that you can do is have a name reference sheet, as needed for the sake of clarification. Usually, academic documents may not have the full surname and usually have the initial, which is quite common. If there is any specific request or clarification, you can get the name reference sheet signed by a notary so that it becomes valid.

Read Name Reference sheet for US admissions Details