lakshmiswetha From personal experience, the legal framework in India or that matter outside India, does not compel any private institution to accept a candidate with a changed name with gazette notification and certificates with different name. Also gazette is not considered a valid identification proof, as it does not contain your photograph.
In fact there is no legal framework existing at all for the trans population - be it education, employment, insurance or marriage - in India.
I would strongly recommend that you objectively ask the institute whether they
1) Will accept a trans candidate with different name than your older certificates
If not, will they at least accept your case if you bring forward 2 references certifying that you are the same person
2) Or they would like all the certificates with a single name, which is your new identity.
Whatever me or you think and the feel about the dysphoria, identity, transition etc, in the practical world, things happen in a very different way.
2 months back a prestigious European engineering institution turned me down - as my new identity and the education certificates do not match.
I don't know where you are planning to apply - hope my answer helps you.