From ancient times to modern fiction, the phoenix has represented innumerable concepts. For the sake of simplifying her roles, I will focus on the concepts of life, death, rebirth, prosperity (both in everyday life and battle), passion (in all forms) as well as the concept of undying love/loyalty. Because of her very nature, she is always searching for a master or mistress that she can ally herself with (see Albus Dumbledore and Fawkes). Once she finds said master/mistress, she is loyal to them until their death. Then, she takes flight and spends a period in mourning before beginning to look for a new master/mistress all over again.
Because of her endless life-span, Phoenix can be taken from any number of canon points. She has seen ancient Egypt and ancient Greece. She has seen empires rise and fall. Her wisdom could prove useful to just about anyone, though she is very picky with whom she chooses to speak to.
Additionally, I may call Phoenix any number of names (and I will try to list them here). All of her names will have something to do with fire: after all, she never tried to hide her nature - even if she was trying to blend in with society for a time. Her core nature will always stay the same even if she alters her appearance to suit her new situation.
And, lastly, in case you were wondering, the idea of Phoenix came from the Harry Potter series. Fawkes has always fascinated me and he prompted me to think about a female phoenix's nature. As such, I decided to create a very old phoenix who is every bit a queen in her own right. Yes, she has had children and yes, she has fallen in love with phoenixes and humans alike. (Though in the latter case, her heart was always broken.) She can choose her form thanks to a spell one of her previous masters put on her. Therefore, sometimes you will see a magnificent bird and other times you will see a mysterious woman. I will always note her form so you will never be forced to guess.
If you have any questions regarding her, please leave them here and I will attempt to answer them!