There are actually a lot of reasons for this trend. Some of them come from Japanese culture, while others come from translation problems. The main reason, though, is a part of Japanese culture. Unlike the US, where shows are given names like "The X-Files" or "The West Wing" that refer to the subject matter or some general element of the show, many Japanese TV shows are named for the main character, a la the US's "Buffy the Vampire Slayer". Thus, Japanese culture tends to name a show about a school "Great Teacher Onizuka", after the main character Onizuka, instead of just naming it after the school it's at, or calling it something generic referring to education.
The second, and much more diverse reason, is the way anime is translated into English. One major part of this is that many anime series come with their own English titles, which have been added by the producers of the show or the company that owns it. This practice has spawned names such as "Neon Genesis Evangelion" and "Martian Successor Nadesico". The other problem with the translation is that American translators some times have to do their best to fit the original title into English. The closest thing they can manage to "Kyuuketsuhime Miyu", which literally translates to "--Single Word Meaning Princess That Sucks Blood-- Miyu", is "Vampire Princess Miyu". Because many Japanese words translate into a two word adjective and noun set in English, and many anime titles are translated as literally as possible because the fans have been very outspoken about wanting them translated that way, you end up with titles like Vampire Princess Miyu.
And finally, the last, and very common translation problem, is that of the way Japanese wording translates into English. This is something that is common in all translations in and out of English. If you took The X-Files and translated it to Spanish, it would probably be translated into something like "Los Ficheros de X" (literally: "The Files of X"). This is similar to what happens in Japanese-to-English translation. When translated literally, the wording will seem a little strange in English, and you end up with things like Revolutionary Girl Utena, Mobile Suit Gundam, and New Mobile Report Gundam Wing.
It should be noted, however, that many anime series do not follow this pattern, though it is more common to name a show after a character in anime than it is in the US. Neither follows a strict naming convention, but instead follows a relative pattern "most of the time".