A person’s name has their personal identity is linked with it and one’s professional identity is also completely entangled in it. In India, it is not necessary for a woman to change her maiden name after marriage. If she decides not to change her name and to retain her maiden surname, she should continue to use her maiden name everywhere, for licenses, accounts, insurance, in the work place, PAN card, voter card, NASSCOM card, credit cards and legal documents. She cannot begin to adopt her husband’s surname in these documents after choosing to retain her own surname, to avoid confusion. The purpose is that her identity should be unique. She must be identified by a single name.
A wife who has not changed her name after marriage may continue to use her maiden name by publishing in the official gazette. As long as this requirement is taken care of, she can even file court proceedings maiden name. If she retains her maiden name, a woman cannot be forced by a court to write her name as her first name followed by her husband's first name and his surname while making a marriage-related petition. (Source: The Economic Times Mumbai, March 10, 2008, Page: 17, “Nuts & Bolts of a Name Change”)
Retaining a maiden name in the passport and continuing to hold the title of “miss” and “unmarried” does not amount to misrepresentation or fraud. If the passport is issued before marriage, there will be no reason to change it. Provided, this is only if one is not changing her name after marriage. If a woman changes her name by adopting her husband’s surname, it will be necessary to change it in their passport and update their marital status by renewing their passport.
She must use her maiden name on her VISA application as well if she has retained the use of it. However, if she has mentioned her marital status in forms such as VISA application, etc., then it is better if she carries a copy of her Marriage Certificate with her to avoid discrepancies. (Source: FAQ Section, Passport Seva, Consular, Passport and Visa Division. Website- http://passportindia.gov.in/)
It is legally and practically desirable to have one unique name in all identity-related documents, be it in the passport, voter card, PAN card, Adhaar card or bank documents etc. If it is not so, the same has to be explained by way of an affidavit. This applies to name. However, in the case of your friend, it is a question not of name alone, but also of her marital status.
It appears that your friend has been in possession of a passport before she got married and if she has not changed her marital status in any other identity related document (which displays marital status), then practically speaking, she needn't change it right now and can travel (at her own risk though). As far as surname is concerned, our laws allow a woman to retain her maiden name even after marriage.
Needless to mention that it is always risky to travel with or use a document which does not disclose accurate information. In case of a passport, it is not only a document facilitating travel but also an important proof of identity. For instance, if there is a future dispute with her husband, possession of a passport in her maiden name and travelling subsequently without the disclosure of marriage may become a contentious issue for various reasons. Discrepancies in marital status in passport and other documents may create a legal hurdle. In fact there may be innumerable situations where it could lead to a future problem.
Therefore, if she wants, she can travel, provided not a single proof of identity or other official document (which displays a marital status) has a different status, but even then, at her own risk, however small. The better thing would be to re-issue the passport as soon as possible, updating the marital status and do the same for all identity-related documents. If there is disclosure of marriage while applying for visa, it may necessitate production of marriage certificate. One can refer to the official website of Passport Seva, Consular, Passport and Visa Division, Ministry of External Affairs, Govt. of India - www.passportindia.gov.in for more information.