Unlike speeches and books, court cases don't have much wiggle room when it comes to titles. The title of a case is set by the judicial system, and it's always a "versus" title. As in, someone versus someone. Whoever's being taken to court (for example, being sued, or being tried for murder) comes second, and whoever was harmed (the person suing, or the family of the person who was injured) comes first. So in the case of Miranda v. Arizona (the "v." means "versus"), Ernesto Miranda is taking the state of Arizona to court (through his lawyer, of course).

But wait, the whole state of Arizona? Was Miranda suing millions of people?

Not quite. Basically it means that Miranda was challenging the Arizona law or justice system. You gotta love living in a nation where one individual can do that if they believe their constitutional rights were violated.