I would simply call that a branching logic form or a conditional form. It is also the underlying principle behind a "wizard" style interface: the user is given one choice or option at a time, and based on the results of that choice/option they are given the next. This can be done in sections of a form that are progressively disclosed, or one panel at a time. Ideally you plan this out by creating a workflow that shows all of the options and which option takes people where.
For classic examples of how this works, play around with a free Google Forms or Surveymonkey survey and add conditional logic to some of your questions.
Or pick up a Choose Your Own Adventure book! ;-)
Ok - found one example. This registration form all takes place on one screen. The users first tell us what country their organization is in:
Depending on the country chosen, the fields are different. For example, if they choose USA, they see these:
And if they choose a different country, the options are different (apologies for the placeholder content, this was a work-in-progress):
A simple example, but you gret the idea. The down side is that it requires more coding and a heavier page to include all of the options on a single page. But you could put whatever information and/or questions you want on each of those states, and continue that down the page until you get to your final presentation of information.