Complex sentence: Most people living in medieval Ireland would not have belonged to any Clan, even if they shared the surname of a powerful lineage, that would not have been a qualifying criteria for membership of the Clan in any meaningful sense.
Split into simpler sentences: Most people living in medieval Ireland would not have belonged to any Clan. Even if they shared the surname of a powerful lineage, this would not have been a qualifying criteria for membership of the Clan in any meaningful sense.