Srila Prabhupada says:
Krishna Consciousness is not a faith, such as the Hindu or Christian faith, but it is a science. When Krishna says dehino smi yatha dehe…, the principle is that the soul is different from the body. On account of the presence of the soul we are getting different bodies. You cannot say it is Hindu. The Hindu religion may be more advanced, but Krishna Consciousness is a science. Others have only a vague idea. Krishna never said He was preaching as a Hindu or for the Hindus.
But as a public statement you may say we are part of the Hindu dharma. It is actually Vedic culture, but they have been misinformed. We are actually Varnasrama dharma. The public doesn’t understand Varnasram so sometimes we say “Hindu dharma. “It is a great science but unfortunately the name has come since the Mohammedans called the Indians Hindu because of the Indus River. The word is coming down like that, but we do not find the word Hindu in any scripture. Letter to: Pranaba, 1 February, 1977