In Israel, people of Iraqi origin will usually use butnaj/butnuj to refer to Micromeria fruticosa (Zota Levvana in Hebrew). However, I will not be surprised if in Iraq it refers to a different plant.
It is used to flavor cooked fava beans, kebabs (mint is more common now, but I believe it was the original spice in Iraqi kebabs). It is often paired with cumin. Like mint, it makes tasty tea, especially with strong black tea.