Ask the relatives of this person, if you are familiar with them. If a woman has brothers or unmarried sister, then you can directly ask her, what's their name, not calling immediately suspect.
If you are aware of the address of the woman, and that she was not unfaithful after marriage, find out the name in the telephone directory or databases that were published during her girlhood. You can also use the new directories, if you are sure that the number is registered to her parents.
Visit one of the sites who have information about former and present names of citizens. For example, If information about this person on the website yet, you can request the appropriate help (for a fee) only in the case if you have at least some coordinates of this girl.
Go to one of the social networks on the page of this person. It is possible that among his friends are those who know his mother's maiden name or the name of his mother.
Ask for any purpose the marriage certificate of this woman. It is better that the objectives were clear and simple. Imagine, for example, an employee of the housing office or the courier of the tax service. Even citizens, really working in such positions do not always require certification, especially since they are not always issued and similar institutions. This method will work only if you are aware of the address of this person, but you are not familiar with it, and learn in the future not going.
Contact private detective Agency with the appropriate request. But be prepared for the fact that in our country there are principal investigators who are concerned about the confidentiality of personal information. The cold reception you can expect to also have the passport guy, the registry office employees and other official institutions.