Throughout the book Speak by Laurie Halse Anderson, the reader learns that Melinda gives a lot of characters nicknames. Melinda does not give nicknames to everybody she comes in contact with, though. She only gives nicknames to people that she does not like or respect. Her English teacher, for example, is called Hairwoman. Another character that Melinda doesn't feel is worthy of calling by name is the Guidance Counselor.
Principal Principal is the name that Melinda gives the high school principal. Melinda has no strong feelings about him either way, which is why she calls him Principal Principal. He is nothing more than a functionary of the school. He is his job, not a person. He's an automaton of sorts in her opinion. The reader comes to agree with this assessment of him as well. He's not a bad guy. He does try to connect with students, but is completely inept at doing it. He is best left to his own devices as an administrator, letting his teachers (like Mr. Freeman) find ways to connect with students. Considering his ineptness and what Melinda named other characters in the novel, Principal Principal should be glad his nickname wasn't worse.