Yup, that's how you start a new game/delete an old one in Diamond/Pearl. It's kind of a shame that you can't have more than one save file. I wanted to start over and had to delete my first game file because of it. I guess that prevents two people from sharing a game, but then again if they wanted to trade pokemon or something, they'd need two Nintendos anyhow, I guess.
I was kind of wanting to restart yet again, because my trainer name is written in Japanese and that might pose problems when trying to trade/battle with folks. But I've spent a decent amount of hours already and don't wanna delete all my work.