If I change my name/city name, will they still be able to trace the old name and they will know it..

It depends. If someone sent a e-mail to you or you sent e-mail to anyone before you changed the name - after changing the name such person will have those e-mails under your new name and under your alliance. So in that way this is easy to track your new name. This is the only way I found to track it.

Yes, the game glitches. People will sometimes see your old name when you chat in state chat. Or when you text. Also if they sent you an email and saved it they will trace your new name. Also I have deleted emails and log back in only to see the emails I delete still there. The game offer no real protection from that because of all the glitches