Could the contact be from another source that isn't editable on the phone? I know some my contacts that are sourced from Google+ are not editable on the phone.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
Sorry for this inconvenience. Does your device have any physical or liquid damage? What source are you using to back up your contacts? Are you able to edit that contact from Verizon Cloud, Blackberry Desktop Manager, or a third party application?
Follow us on TWITTER @VZWSupport
If my response answered your question please click the _Correct Answer_ button under my response. This ensures others can benefit from our conversation. Thanks in advance for your help with this!!