Hourai is a legendary island paradise in East Asian folklore, which was said to be inhabited by immortals who had special powers, and possessed rare treasures as well as the elixir of immortality.
She so far has no known relation to either the Hourai Elixir or Kaguya Houraisan, nor even to Mokou, who also has a spellcard called "Hourai Doll". It is most likely a reference to the aforementioned island paradise of Hourai, since Alice's other spell cards (such as Foggy London Dolls or Red-haired Dutch Dolls) are references to countries or cities.
As with Shanghai, Hourai is canonically a class of doll rather than a name for one individual doll, and multiple Hourai dolls are seen during its spell card in PCB.
蓬莱, the kanji for Hourai, is another name in Japanese for Taiwan, Penglai. Meaning both of Alice's dolls are named after Chinese locations, Shanghai and Penglai.