Why they name it progressive era? if they can just say the Great Depression because they are mostily talking about how people where depressed and fighting for constitutional rights.?

It was called the progressive era because many of the ideas that arose were considered very modern, educated, or progressive.

The Great depression was called a "depression" because our economy was going downhill after the market crash in 1929. Basically, it has to do with our economy suffering a downturn where almost everyone was struggling economically.