The upper house of a state legislature is usually called

An upper house, sometimes called a Senate, is one of two chambers of a bicameral legislature (or one of three chambers of a tricameral legislature), the other chamber being the lower house. The house formally designated as the upper house is usually smaller, and often has more restricted power, than the lower house.

The upper house of a state legislature is usually called the Senate.

Explanation:

In most governments that have a bicameral legislature, there is an upper house and a lower house. The upper house, which it's also smaller in size and has longer terms, is usually called the Senate.

The United States' upper house, for example, is the Senate and it is composed of two senators per state which makes it smaller than the House of Representatives (the lower house) whose number of members depends on each state's population, and therefore, it is larger. Also, the Senate also has particular powers that the Houses do not have such as the power to conduct impeachment trials, to advice, approve or reject presidential appointees to executive and judicial branch posts and to approve treaties made by the executive branch.