I know people from ISKCON that legally changed their name.
ISKCON doesn't like to be grouped in with the Hindus because so many Hindus just approach their religion in a materialistic way. They have no appreciation of a transcendental objective to their practices, and have no conception of pure bhakti. Srila Prabhupada didn't want to get grouped in like that.
Sure, Bhagavad Gita is a beginning book for ISKCON members. But also we have Bhagavatam that teaches Krishna's pastimes and Caitanya Caritamrta which teaches how to worship Krishna as Radhika dasya. These things are beyond most "Hindus" who just want to make lots of money and move to New Jersey.