Was what I did correct when I lied to a girl using my friend's name, then repented and told her that I had used my friend's name, and do I have to apologize to my friend?

All praise is due to Allah for your repentance. You must repent to Allah with sincere repentance and frequently seek forgiveness for your friend, and supplicate for him with good, because of what you did in impersonating him to exonerate him. There is no need to inform him of what happened.