Some middle eastern countries use family surnames in the last place, like Western names. Although this is a recent convention; it isn't historical. Historically, surnames from most of the middle east referred to a placename, much like the origins of surname in Europe.

"Saddam" is not a name, it's a title. Hussein al-Takriti is his given name (i.e. Hussein of the town of Takrit). Saddam was adopted as kind of a political name, and it means, roughly "the Destroyer."

Technically, we should use the full "Saddam Hussein" ala Ivan the Terrible or Richard the Lionheart.