The correct romanization of Alice's surname ought to be Murgatroyd, as ZUN intended her surname to be the same as Miss Murgatroyd from an Agatha Christie novel. However, this surame could not be written properly in katakana/kanji, so when the translators translated the Japanese version of the name back to English, they made her Margatroid since they probably missed the Agatha Christie character reference. Please refer to her by her intended surname from now on.
This surname still exists, and is most common in England, where it originated in Yorkshire. Alice is most likely a Yorkshire-woman.