Connotation is everything. Prostitute is very technical and clinical and even though it's a profession (and a legal profession in LPIN) to the mainstream it carries stigma. I know very few people in LPIN who will proudly say "I'm a legal prostitute!" because generally the response just isn't the same as even "I'm an exotic dancer!"
While "Hooker" may commonly be used by Hof PR, Ladies who do not work his houses and even some Ladies who do - are not fans of the word. Again, because of connotation and stigma. I've only ever heard "hooker" used among Ladies in self-deprecating humor.
Since being a courtesan isn't all I do I just like to jokingly tell people I'm myself for a living - because I do s many things. But for those where this is their main job and all they do the job title should reflect that with as little stigma and as positive connotation as possible (in my opinion).
I liken myself to historical figure Madame de Pompadour, especially how she was depicted in the Doctor Who episode "Girl In The Fireplace"-
"The Doctor: [quiet and confused] Poisson?...
[shocked and excited]
The Doctor: No, no, no way, Reinette Poisson? Later Madame D'Etoiles, later still mistress of Louis the XV, uncrowned Queen of French? Actress, artist, musician, dancer, courtesan. Fantastic gardener!
French Servant: Who the hell are you?
The Doctor: [triumphant] I'm the Doctor, and I just snogged Madame de Pompadour!"
Madame de Pompadour, historically, was a French prostitute and paid mistress of King Louis the XV (but because, well, French, she and the actual Queen got on fairly well). But she was a lady of other skills and talents who just happened to also have a talent for sensuality and sexuality and profited from her services. Like the modern Lady, Reinette Poisson was more than just a sex worker. She had a life and depth to her beyond that one aspect of herself. The term "courtesan" sounds nicer and more respectful to her as a full person in that regard. The same as I feel it does to us in the modern era.