The country singer, who called off his planned divorce from wife Tish in March, explained that he chose these names because he had a "vision" that she would inspire people.
Asked if he would stop her pursuing fame if he had another chance, he replied on Piers Morgan Tonight: "This was Miley's dream. This was her - I believe to touch people's lives. Through her music and her life. I still believe that. You know, her name was originally Destiny Hope, I had given her the name before she was born because I had a vision. I felt it was her destiny to bring hope to the world.
"When I see her selling out arenas around the world or on her TV show, making people laugh, bringing families into the living room together, we always, you know, try to put positive messages in each episode if we could. And, you know, I do think that she - this is her purpose - her path."
Billy Ray also said that his 18-year-old daughter - who got her name Miley from adapting her childhood nickname 'Smiley' - is a very loving person and does her bit to help others.
He explained: "I think she's a natural born singer/songwriter/entertainer. She's a great actress. And she's got a lot to offer the world. She's the real deal. What you see is what you get. I mean, she's for real.
"And, you know, she ain't perfect and I sure as hell ain't, you know. I mean, none of us are. But Miley really, really has a good heart. And she loves people. She loves music. She loves entertaining. There's a lot of things that Miley does that I wouldn't go into right now on a humanitarian basis. But Miley is a great humanitarian. She really cares about her fellow man, and people, and the planet and animals."
Billy Ray recently said that his family is attempting to put aside any past struggles.
Watch Billy Ray Cyrus's music video for 'Runway Lights' below: