Even though she has no official profile and has only made two appearances in gameplay (and even then only as a spell card), she somehow become a very well known character.
The name Shanghai, or Shanghai Ningyou, is a reference to one phrase of Yellow Magic Orchestra's music, "Chuugoku Onna" (Chinese Woman, 中国女. Official counterpart is "La femme chinoise", only the title of which is a parody of Jean-Luc Godard's "La Chinoise"); "For Susie Wong and Shanghai dolls".
The red-dressed, laser-shooting doll in front of Alice while focused in Imperishable Night is Shanghai.
In Shanghai's first appearance in Perfect Cherry Blossom there were actually several Shanghai dolls that appeared all at once, causing some to believe this is simply a type of doll rather than the name of a specific doll. Supporting this, Shanghai has never been used as an individual name for any doll in canon; the term "Shanghai doll" is used instead.