What is the name for a question that decides what further questions to ask?

When I was working as a QM for some local BPO's, we used to use SurveyMonkey to create formats like that.

It is sometimes referred to as...

skip logic

Skip logic is a feature that changes what question or page a respondent sees next based on how they answer the current question. Also known as “conditional branching” or “branch logic,” skip logic creates a custom path through the survey that varies based on a respondent’s answers. This skip pattern will vary based on rules that you define for the respondent.

-SurveyMonkey.com

The particular type of question is often called a..

Branching Question

A question used to guide an interviewer through a survey to different questions (i.e. skipping some questions), depending on the answers given.

-Insights Association