What was the name of the *other* Spartan king during Leonidas's time?

Factual Questions
1

As many of you know, Sparta was ruled by two hereditary kings simultaneously.

Every one knows Leonidas, but who was the other one? What was he doing at the time of the Persian War? I know that Demaratus had been a recently deposed king, but was he replaced by the time of Thermopylae?

Anyway, if government by one king is called a monarchy, what is a government by two kings called? A dualarchy? A binarchy?

2

Leotychidas. He’s most famous as the victor of the battle of Mycale, which, along with the battle of Plataea, ended the Persian War.

3

It’s generally refered to as a “dual monarchy.”