As you probably know alias means "also known as". In other words the person was known by more than one name. Aliases were used in cases of illegitimacy, upon the remarriage of a parent, [i.e. if a mother remarried, her children might take the name of their new stepfather, with their original name as an alias - or vice-versa]; upon inheriting property from a female relative, etc.; to differentiate between different holders of common surnames; to indicate stepchildren or fostered children. In some cases the alias form was inherited for several generations, and was similar to a double barrelled surname Discovering the reason for an alias is not straightforward, and each case has to be treated on it's merits. Even in cases of illegitimacy there is no rule whether the father's or the mother's name was given first.
Stan