The words you might want are co-regents, or co-monarchs. The government might be called biarchy or diarchy (Sparta) or duumvirates (ancient Rome) Co-rule in general is actually quite common.
Hungary had dual kingship for a while at first; one a religious leader, one a war chief. (Division along these lines seems common.)

William and Mary were co-regents of the Kingdom of England, Scotland, and Ireland, but a married couple (also first cousins to each other.) Mary II had the actual claim on the throne, but was already married to William who was a prince. So it was appropriate to make him a co-regent too.
They became so after agreeing to the Declaration of Right drawn up by Parliament that restored the Monarchy-- as a limited, constitutional monarchy. King James II had abdicated by abandoning the country. They were also Protestants and they wanted that, not Catholics.

There have been other co-regents, often a parent acting for a minor child not yet of age to rule.

Two co-kings in Europe- the closest would be the co-rule of Frederick I of Austria and Louis the Bavarian over the Kingdom of Germany. That was a complex situation that is worth reading about.