changing apple ID on devices

My family has an iPhone, 2 iPods and an iPad. I recently updated my email address and my Apple ID to show that new address. However, the old address still often shows (not always!) on the different devices as the Apple ID. This is an unchangable line of text that automatically shows in the login window, with a box below to type in the password. Then when I try to log in, it either gives me a "wrong password" error (and I don't remember the password associated with the old address/ID)...OR, it says there is no such Apple ID. And then, sometimes it works! And then sometimes I fumble around long enough that I can get an ID textbox to change it, and then all is good...but it eventually reverts back to the old ID associated with the device. How do I get it to stay PEMANENTLY changed? It is changed in iCloud....

Also, how do I change the name of a device (say from Sue's iPod to Sally's iPod)?