You can keep your own religion - Buddhism, Islam, Hinduism, Mormonism - you just need to add Jesus to the equation. Then you become complete. You become a Buddhist with Jesus, a Hindu with Jesus, a Muslim with Jesus and so on. You can throw out the term Christianity and still be a follower of Jesus. In fact, you can throw out the term Christian too. In some countries, you could be persecuted for calling yourself a Christian, and there is no need for that. Just ask Jesus into your heart, you don't have to identify yourself as a Christian.