Will it be a problem in getting H1B as i have changed my name after college?

Hi, I have changed my name completely on Sep 2013. My old name is Jayanthi Baskaran and new name is Sidikshashri Baskaran. I changed my name in TAMIL NADU GOVERNMENT GAZETTE and published in Newspaper(Both Tamil and English). My passport is having my new name only.The other proofs like Voter Id,Aadhaar Card,Birth Certificate,Pan Card,Marriage certificate are also having my new name.But 10th,12th and Degree certificates are holding my old name. I have contacted university for changing my name but i have been told that its not possible to change. Will the Gazette Copy holding new name would be considered here in USA as a valid proof for name change? Will it be a problem for me to work in USA? if the names are different in the Degree certificates(old name) and new names in others documents like passport etc. It would be helpful if i get an answer for my query. Thanks, Sidiskha.