It comes from a 7th century Christian Orthodox monk and theologian called Maximus the Confessor who has a good reputation among Christian Orthodox faithful. https://en.wikipedia.org/wiki/Maximus_the_Confessor
It may be the name he provided as his legal name when applying for visa/permit. Patronymic name is foreign concept for US/Canadian legal system so for immigration purposes it is treated as middle name AFAIK and quite liberally at that.
Canadian immigration service, for one, just cuts patronymic name if total length of first + patronymic + last names exceeds certain limit (my guess - the limi tis length of the field in some form/database). So "Igorevich" becomes "Igore" or "Igorev" depending on you first/last names lengths. US may have more flexible rules and lets you provide your version of middle name or drop it altogether.
I wouldn't attach too much importance to this detail
There are no patronymics in Russian passports at least, not sure about Ukrainian. But even if they are, it would be Igorevich 100%. And it's always written on American visas as in national passport.