Since Bahodir Fayozov is a proper noun, it should be capitalized: Bahodir Fayozov — "Chiroyli qiz" .
If you are looking for the "proper" or grammatically correct way to write or use this phrase, it depends on what you mean: bahodir fayozov chiroyli qiz
The phrase translates from Uzbek to "Bahodir Fayozov beautiful girl." Since Bahodir Fayozov is a proper noun, it
To say "The girl is beautiful" in a full sentence, you would write: "Qiz chiroyli." you would write: "Qiz chiroyli."