At its core, “clan” refers to the children of a chieftain. However, a clan includes more than the biological descendants of a chief. Followers a clan chief, regardless of ancestry, would become members of a clan. Before the arrival of the Normans, male Scots and Irish would be known as their father’s son. Thus the son of David might be mac David. Scandinavians used similar name protocols. A man named Olaf might have children called like Olafsson or Olafsdottir. With the adoption of “surnames” followers of local chieftains may have adopted their names even if they were not blood relatives. In other words, a clan was more than DNA. It was familial and tribal.
Today, there being no clan chieftain, it seems that any descendant of McCullochs (in all of its spellings), whether from paternal or maternal lines, might consider themself part of Clan McCulloch, and be accepted as such.
Short of taking a Y DNA test as described here, a descendant of Scottish McCullochs or Irish McCulloughs may not know if they are a descendant of the Galloway McCulloch line. But, even if one is not a member of the same Y DNA haplogroup doesn’t settle the issue of identity, affinity, and what might quite loosely be called kinship. Again, not all clan members were related by blood. So, it seems that other “Scots-Irish” McCullochs, McCulloughs, McCullohs, et al who identify with the clan should be accepted by the clan. Because the origins of each of these names remains a mystery, there is no way of knowing whether our ancestors, though sharing no recent common ancestors, may have viewed themselves as members of a common tribe.