Since the daughter is born in Surat district, Gujarat, you have to approach the competent authority for births and death registration within the jurisdiction where your child took birth with an application for change of name in the birth certificate, if the authority refuses to accede to your request, ask them to give the same in writing and then approach the jurisdictional court with a suit for declaring the correct name of your child as proposed by you now, alternately, you may make an affidavit stating that both the names are one and the same and she will be hence forth called as 'so and so' and on the basis of this affidavit, you may get the same published in the government gazette at Mumbai itself, you may also publish the change of name in the local newspaper too which can be attached with the gazette publication after which she can be called by her new name and the same may be registered in her school records too at a later stage. For all these, you don't need the help of any advocate or an agent, you can do it yourself, but in case you are too busy or not able to find the proper procedures to be complied, you may take the assistance of an advocate in the local.