Keeping the surname in brackets is something that I have not heard of. As far as passports are concerned, international travel and visa needs clarity of name. In these circumstances, the name format is very clear. First name, (+/-) middle name and last name or surname.
You can do two things, if the travel is only for a short holiday, use the current valid passport with your wife's existing name.
If you want to change it before travelling, you need to decide on what your wife's name is Mrs X Bose Choudhury - first,middle and surname (WITHOUT ANY BRACKETS) OR Mrs X Bose - first and last/surname or Mrs X Choudhury - first and last/surname.
Then go the the nearby Notary and make the name change affidavit clearly mentioning your wife's name. Then please publish it in one local English and one Vernacular daily newspaper. Please keep the newspaper cuttings of the two name change announcement in hand. Once this is done, then correct the name in the Marriage Certificate also.
With all the new documentation, then approach the passport office for the name change. I would also suggest that you search for the near by passport seva kendra (https://portal1.passportindia.gov.in/AppOnlineProject/locatePSK/locatePFCInp) or teh district passport cell (https://portal1.passportindia.gov.in/AppOnlineProject/locateDPCSPC/locateDpcSpc) and meet the deputed officers who can help you further.
If your wife is joining you abroad for work or citizenship etc, then please ensure that all her other Identity documents, bank accounts, date of birth certificate and education certificates have her correct name with respect to the timeline before and after the marriage.