Why did they name the case Brown v. Board of Education. They were all 5 cases but why did they name that case Brown v. Board of Education?

Be sure you're clear on what a class-action suit is.

http://www.answers.com/topic/class-action-suit

http://en.wikipedia.org/wiki/Brown_v._Board_of_Education

The case that is commonly referred to as "Brown v. Board of Education" is actually a collective name given to a set of separate cases that were consolidated by the U.S. Supreme Court. The reason it is known by this name is because the lead case in the group had that particular name. Let me explain further on how the name came about:

In the early 1950s, a series of lawsuits were filed against various educational institutions challenging racial segregation in public schools. One of these cases, initiated by the parents of Linda Brown, a young African American girl from Topeka, Kansas, became the most prominent. Linda Brown was denied admission to her local elementary school, which was limited to white students only, on the basis of her race.

When the group of cases reached the Supreme Court, it was decided to consolidate them into a single case for a unified decision. The lead case, officially named "Oliver L. Brown et al. v. Board of Education of Topeka, Shawnee County, Kansas et al.," was commonly referred to as "Brown v. Board of Education" to represent the collective group of cases. This naming convention allowed for a more concise reference to the landmark Supreme Court ruling that ultimately resulted in desegregation efforts in U.S. public schools.

Therefore, "Brown v. Board of Education" is the name associated with the lead case of this consolidated group, which played a pivotal role in the legal battle against racial segregation in American education.