In the original Pokémon Pearl and Diamond games, the Pokéch used to fit in the lower screen on the DS, but in the Pokémon Brilliant Diamond and Shining Pearl remakes, the Pokéch fits in the top right corner of the screen.
I for one find it to be very annoying, even when it is shrunk down to be in the smallest size, especially when I play in handheld mode. However, it is possible to completely hide it! Here's how you do it:
To completely hide the Pokéch, simply hold down the R button for about two seconds. This completely hides it, and you can press the R button again to get it back. This is super useful for when you want to have the entire screen for playing.