I'm pretty sure the "Prime minister" IS Zed. Which is why he sent Olivia to the opposite kingdom, so between her slaughtering and his "guiding" of the king there can be many "unfortunate" deaths.
Especially if that family name she picked was from the kingdom Olivia is in and actually has ties to him like maybe as a "disguise" for himself some time in the past or maybe somehow he was human an eternity ago. It's also possible he "set up" that family name sometime before or after he "disappeared" specifically for Olivia, knowing she would pick it especially with that jewel. "Convincing" the people in charge to "create" that family name and emblem probably would be easy since he's a God of Death.