# The one who conquers

“anyone who is victorious” or “Those who win the fight against sin”

# will be clothed in white garments

"will wear white garments" or "I will give white clothes"

# I will confess his name

"I will announce that he belongs to me" 

# before my Father

"in the presence of my Father"

# my Father

This refers to God the Father. It is best to translate “Father” with the same word that your language uses to refer to a human father.