Is there somewhere I can write my name on iPod touch, for if I lost it?
No, but you can create an image that has your name and contact info on it, then use that as your lock screen wallpaper.

You could also create a note on the device or an "emergency/lost" contact in the address book, but both of those require you to not use a passcode to use the device. A wallpaper with contact info works even if the person who finds your iPod can't unlock it.