Phuong is the name of a character in Graham Greene's novel The Quiet American. The name's meaning is mentioned in the book; she is a young Vietnamese woman who represents a phoenix in many ways.
Phương (芳) does not mean "direction" but "fragrant; virtuous; beautiful". cf. http://nomfoundation.org/nomdb/nom_details.php?codepoint=82b3&img=1 the homophonous phương (方) "direction" is not normally not used as a given name. Phượng "phoenix" differs in tone so they are not hard to keep apart.