Having last name in Passport is very important. You can take the exam, ETS may allow you take the exam and you could get away. But, it is a much bigger problem to have a blank surname. Get your passport fixed with right first and last names. Read Blank Last Name in Passport - Issues How to fix .
I gave a different opinion from Kumar in a similar question. In any case, a ‘one and same person’ affidavit will be helpful in case there is confusion.
All the best
Dr. Sandeep Shankar, Colorado Heights University, Denver, CO 80223, USA. www.chu.edu; sshankar@chu.edu