When a client computer wants to connect to a service instance, what specific name type does it use to find the service?

The answer is "Service Principal name".

Explanation:

It is also known as a prime service, that need a unique product in various reasons descriptor, and also provides the static routing protection, that enables you to use SPNs.

It also enables a client app to demand a transaction authentication by the provider, even though the customer may not have the username and password. It connects a system instance with such a company logon account, that's why it is the correct answer.