Yes, double click on the name of your iPod (under devices) and it should give wewe the renaming box. I'm sorry if that was a pretty poor description, but hopefully someone understands me.
Yes. Plug it in and wait for it to appear in iTunes and click on the the current iPod name until it turns blue and fill it in with whatever name wewe want.
Plug your ipod into your computer and have itunes opened. wewe will see a ipod ikoni on the side toolbar that will have our name of what ever your ipod in called now. wewe click on that ikoni to highlight it and then click it again. wewe should be able to change the name.