To elaborate on what's already been said, "Alice" cannot be written/spoken in the Japanese language. The necessary combinations of sounds simply do not exist in Japanese, the same way the Japanese "r/l" and Chinese "p/b" sounds do not exist in English. "Arisu" is the closest thing you can get.
Yeah, I know it can't be pronounced by the average Japanese person, but I still maintain that if they wanted to name her that it would be 'Alice' (roman letters) on her birth certificate. ... I'm probably just being stubborn though.
... I'm probably just being stubborn though.