Isn’t Lucifer not Satan?

They are the same. However, the name “Satan” is used exclusively of the evil one. It means “accuser” and refers to his constant accusation of the brethren before God. The name “Lucifer” means “light-bearer” or “morning star” and so is used also of Our Lord, as in the Easter Vigil’s Easter Chant, or in the blessing of holy water late, and is even the name of a saint in the Martyrology, St. Lucifer of Caligliari. So you could name your son Lucifer, and it would be a saint’s name! (I wouldn’t advise this, however, since we want the child to have a happy childhood!)