Is there somewhere I can write my name on iPod touch, for if I lost it? Where in my iPod Touch I can write my name and phone number, so if I lost it or it been stolen and found by the police (as I read that happened), someone could call me to go get it back?
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.