The "alias" could mean anything. It might be her maiden name, or Fields could be (unless you KNOW otherwise). She could be a widow and Willims could be her former husbands name.
Or it could be a true alias. Just another name that she used for some legitimate reason.
Did you find any other "alias" in the marriage records. If so, you might post to those Boards (or lists) and question those names. That may provide your answer.