It appears that you are talking about India ... a country that has, to be nice, has 'strange' rules.
What name does her birth certificate have?
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You would be best advised to indicate her legal name. This is the name typically on the person's birth certificate or passport.
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In the application indicate her legal name, also disclose all the names she ever used, including the one on marriage certificate with dual last name. You should not have any problems, this is a typical situation for some countries. Later on you can have her name legally changed.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.