Wu Hao
The fourth tone of Hao Nian HAO. It means vast and boundless, and also refers to the sky. When combined, it means boundless, which indicates the acceptance of all things, broad-mindedness, and popularity. Of course it's fine.
I think this name is pretty good, even though it only has two characters.
Or if you insist on three characters, just call it Wu Haochen
Chen means morning, he was born in the morning, and he is a rooster. The rooster often crows in the morning, which means a new beginning.