Q: changed to new email address on itunes, but old email address is showing up on the new phone

Hello Sharon,

Congratulations on your new iPhone 5c!  If you are seeing your old Apple ID on your new iPhone, you can log out of one Apple ID and sign in with the alternate Apple ID in a few different locations in settings to update this.

If you are trying to sign into the iTunes and App Store with your Apple ID, you can use these steps:

Changing your Apple ID account

Tap Settings > iTunes & App Stores, then tap the Apple ID signed in.

Sign out of the current Apple ID account and then sign in with another account or create a new Apple ID.

You can find the full article here:

iOS: Changing the signed-in iTunes Store Apple ID account

http://support.apple.com/kb/ht1311

I also recommend signing out of FaceTime and Messages.  Once you are signed out, you can sign in with the Apple ID you would like to use on that device:

Sign out of iMessage or FaceTime:

• iMessage: Go to Settings > Messages > Send & Receive, tap your Apple ID, then tap Sign Out.
• FaceTime: Go to Settings > FaceTime, tap your Apple ID, then tap Sign Out.

You can access the full article here:

iOS 7: If you're asked for the password to your previous Apple ID when signing out of iCloud

http://support.apple.com/kb/TS5223

If you have iCloud setup, you can use these steps to sign out of iCloud on the iPhone:

On your iOS device’s Home screen, go to Settings > iCloud, then at the bottom of the screen, tap Delete Account.

Once you have removed the iCloud account from the iCloud settings, you can sign in with your other Apple ID.  You can find more information here:

iCloud: Change iCloud feature settings

http://support.apple.com/kb/PH2613

Thank you for using Apple Support Communities.

Best,

Sheila M.