Multiple High Schools and College Admissions

When college admissions are looking at your transcript/application, do they know if you’ve been to multiple high schools or not? And if so, to what high schools?

The reason I ask is that I am currently at an extremely rigorous high school, but, due to various circumstances, will soon have to move to a less rigorous school. Will college admissions take into account how rigorous my freshman and sophomore years were when looking at my grades and courses, or will they simply assume I took all classes at the school I apply from?

Yup, you list all the high schools attended on the common app and other college applications and you list which years you attend each.

Ah, I see! Thank you very much, @Homeless2Princeton !