Caller ID Name

My wife & I have two iPhones on one AT&T account. Her iPhone's name is "Pat's iPhone" but when she calls someone their caller id shows my iPhone's name (which btw also has an apostrophe in it). I read in the forum somewhere that having apostrophes in the phone's name can cause problems but hers syncs ok. I thought to change her phone's name to eliminate the apostrophe to see if that would help. A post in the forum say you can do this when connected to iTunes in the left hand column under devices. The only place I find a devices choice is in iTunes preferences, where it shows both our phones name's backups, but clicking or double clicking on that does nothing whether the phone is visible in iTunes or not. I tried clicking on her phone's name in the summary tab but that's not editable either. Her phone's software is version 3.1, my phone is on 4.0 and the iTunes version is 9.2. In addition to any advice about renaming the phone, any thoughts on the reason for the caller id issue would be appreciated.