Nathuram Godse's original name was "Ramachandra". He got this name "Nathuram" because he has pierced nose (nath) and Ram from his original name.
Previous three brothers died so it was thought a curse on boy so he is treated as a girl for many year to ward off that possible curse. Later when his younger brother came then parents stopped treating him as girl.
He liked Gandhi in school days. Later after school he joined RSS and Hindu Mahasabha. It is debatable when he quit RSS and Hindu Mahasabha. Many says he quit RSS few years before killing Gandhi.
Godse started "Agrani" news paper that later named "Hindu Rashtra".
Godse and his supporters were angry with Gandhi. Their thinking was that Gandhi supported Muslims too much and but those are anti-nationalists. They wanted separate country.