Restoring a used ipod shuffle 2nd generation

When you say "I cannot restore it," does that mean it appears in iTunes when you connect it but attempting to using the Restore button does not work? Or are you saying the the shuffle does not appear in iTunes when connected, therefore you are not able to attempt a Restore?

If you bought just the shuffle without the USB cable, make sure you are using a USB cable made for the 2nd gen shuffle. The USB cable for the 3rd and 4th gen shuffle fits, but it does not work. The connector is different.

I don't think there is a point during a Restore, when you enter Apple ID and password, unless you choose the option to load it with songs after the Restore is complete. Then, you may be loading old purchased songs from the iTunes Store, which had DRM (copy protection), which means you have to authorize your computer with your Apple ID. NOTE: The iTunes Store no longer uses DRM for song purchases.

But in any case, I believe the Restore itself is complete, or your shuffle would not be working, and you may have just canceled out of loading the shuffle after the Restore, and then you manually loaded it.

To change the name of the shuffle, select it in the iTunes sidebar. If the sidebar is not showing on the left side of the iTunes window, from the iTunes menu bar, under View, select Show Sidebar. After selecting it in the sidebar, click on the shuffle's name a second time. It becomes editable. Change it as desired, and press Enter.