Do people... NOT call it drug and alcohol rehabilitation anymore? Is there a different term now?
Also, I think you're in the clear on this one. If the Phoenix House had been, say, some sort of opium den, then it would be like "Yeaaahhhhh... maybe go back and change that." But, I mean, Phoenix imagery and use is pretty common, so...
(Having said that, 'Phoenix House' -would- have been a good name for whatever the Diqiu equivalent of the House of the Rising Sun is.)
"What kind of progeny a powerful, formless cloud of noxious nightmares and spiritual destruction might produce, I dare not even speculate."