Topic: Birth certificate for I 485

Hi Amazon and others, PD: 10/29/2010 EB3 ROW. I would like to have your expert opinion. My birth certificate has my old name: Thomas Mathew. All other documents including passport, educational and employment documents have my current name: Philip Thomas Mathew. As you can see there is not much of a difference between my old name and current name. The name 'Philip' was added a couple of years after birth. Everything else in my birth certificate is correct including parent's names, place and date of birth, date of registration etc. In my passport, there is an endorsement that I was known previously by the name: Thomas Mathew. I don't have any other proof of name change with me. Is there any possibility of RFE on my birth certificate? If yes, what additional documents can I submit in order to prevent the RFE? Will an affidavit from my mother help in this case? Thank you all.