I think the surname is Ukranian and by the blurb below it seems it's spelled correctly.

I found a blurb on the origin:
DMYTRIW is a Polonized spelling of the Ukrainian name that we'd spell DMYTRIV, using English phonetic values to transliterate the original Cyrillic form. It just means "of Dmytro," and indicates that an ancestor was named Dmytro. The -iw or -iv ending is distinctively Ukrainian, corresponding to Polish -ow and Russian -ov, all of which mean essentially "of." So DMYTRIW means "[kin/family/son/place] of Dmytro," and as a surname it would mean "kin/son of Dmytro." The -iw ending is an all-purpose possessive referring to some kind of link -- possibly "[son] of Dmytro," possibly a more general "[kin] of Dmytro." In some cases it can even be a place name, meaning "[place] of Dymtro."