This should not be done lightly and is not a badge of honor. Using trope namers lightly or as a badge of honor is Trope Namer Syndrome and leads to confusion, renaming, and possible deletion of tropes.
A series usually gets to name a trope if it's so widely known for the trope (even outside the circle of nerds) it's basically an icon of it, or if it has a term for the situation that is simply Made of Win. Or if it happens to be the Trope Maker, too. Of course, since Most Tropers Are Young Nerds, we do kinda swing closer to the geek side of things. But whaddaya expect? This is the Internet, after all!
Also, we at TV Tropes don't want tropes named directly after a trope namer, since the trope namer may always get its own page. If they are the Trope Namer, the trope name should reflect the difference, for example "Rashomon"-Style. This is doubly true for characters, who must embody the trope so well that one could point to them and say "Yeah, kinda like him" and other tropers will immediately agree (without having to consult Google in the process). Even so, there is no guarantee that even the Trope Namer will always actually be an example of the same trope.
Keep in mind, however, that calling a work "the Trope Namer" in the initial TLP write-up simply because you took the preliminary title from it (especially if you are naming the trope after a character) is very presumptuous: chances are high that the troper Hive Mind will disagree about whether or not the work is widely known enough to qualify. Of course, such trope proposals aren't technically named yet; the title may be subject to change in TLP if someone else comes up with a better title. (For the purpose of actually finding a better title, see Naming a Trope.)
- Anime & Manga
- Comic Books
- Comic Strips
- Internet (IRC and other websites)
- Live-Action TV (includes Game Shows and Puppet Shows)
- Professional Wrestling
- Religion and Myth
- Theatre (also includes Opera and Musicals)
- Traditional Games (includes Board Games, Card Games, and Tabletop Games)
- Video Games
- Web Animation
- Web Comics
- Western Animation
- Other Media
- Real Life
Sometimes we don't quite get it right the first time, leading to a rename. Any tropes that were renamed from their original name go there (and under the new Trope Namer if there is one), not under their former Trope Namers.