If Patchouli used wood and metal magic together, would she become Alice Margatroid? It'd be a storm of blades attached to wood, not unlike Alice's dolls.
If Patchouli used water magic when it was cold out, would she become Cirno?
If Patchouli used wood and metal magic, would she become Tewi?
If Patchouli used moon magic and moon magic together, would she become a bitch?
Patchouli is an Englishwoman. Alice, on the other hand, is an awful Romanian. There's no way anyone could confuse them like that!