I am a revert girl in the west and want to get married. There is a man (20) willing to do so but I would still live with my kafir parents. I am afraid of them finding out so is it permissible to do only nikkah and not legal marriage?

A Muslim woman's wali cannot be a non-Muslim, so where she has no Muslim wali, the head of the Islamic center or a Muslim judge marries her. Registering the nikah legally is not a condition of its validity, but I highly encourage that you find a suitable husband and consider carefully, not just whoever is willing.