The naming box is an entity on pre-scratch Earth and post-scratch Alternia. It is used to name children on the day they turn 13 years or 6 sweeps old, and was also used to name Alternia. It's become a running gag, that the first name entered is something silly and derogatory, such as Pooplord, Broad, Prick and Buttlass. The character being named expresses dissatisfaction at this, and their actual name is then entered.
The naming box is a semi-physical entity, since Dave was able to cut it in half with a sword, and Karkat with a sickle. It is also seen through Trollian viewports, and so two of the kids' insulting names were typed in by trolls: " " by Kanaya and " " by Sollux. It should be noted that Sollux tried to name Dave before his thirteenth birthday, which the box did not allow. However, when Dave was named, he got the same derogatory name typed in, sans Sollux's typing quirk.
On Alternia the box uses the Daedric Alphabet, and names Alternia and Karkat, though not before trying to give them the names " " and " ." The other eleven trolls weren't shown with their naming boxes; however, the command to introduce them was still called "Enter name."
Honorary Placronym Edit
In the post-scratch universe, it is replaced with the Honorary Placronym, which was engraved when the kids were 13. Roxy and Dirk had them sitting in their rooms. It was still noted that the silly names were attempted first. Jane was first called Barnstench Fartface and Jake Barfbreath Turdsmirk. It seems to be an item unique to the post-scratch universe, and is first seen . On a child's thirteenth birthday, they are finally given a name, which is then engraved on a plaque similar in shape to the original Naming box seen .
Alternately, naming boxes could turn into placronyms when engraved. Though, a naming box seems bigger than a placronym.
Ultimately it is likely that, like its "predecessor" the naming box, it is a narrative framing device, since John signed letters with his name before his 13th birthday. It is, however, also possible that kids are given names when they're born, as is typically the case, and it is merely a post-scratch custom to have their names engraved on an Honorary Placronym when they turn thirteen.