Without a religion as part of one's culture, it is pointless to discuss if someone should or should not identify himself or herself as of the country of birth when one has emigrated. Further, if a person marries a person of the host nation he or she will have problems in defining herself or himself culturally.
I am Vishista Advaitist Hindu first, a statesman of the United Kingdom second, and no longer an Indian. For apart from visiting India to see our relatives we have no plans to return to settle in India. I am not attached to India or even to the United Kingdom. I am attached to my dharma.