Name on travel document does not match name on passport

My son was born in the US and holds an US passport. We are applying for a Travel Document for him to go back to China with us, but the problem is that his US passport has a different name from his birth certificate because we changed his name. Chinese consulate will only issue us a Travel Document in his birth name. How will this affect us once we are in China? Will my son be prohibited from entering because of the name discrepancy? What if I bring a court order to explain the discrepancy? Is there anything I can do ahead of time to prevent it?