Are you editing it in the only place the information is stored?
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
It sounds like it is being restored/synced with a backup source (cloud?).
It's important your contacts update as needed, dberry1052. Let's take a closer look into what's going on. What is the make and model of your phone? Are you backing up your content with the Verizon Cloud or any other backup source? Are you editing the contact from the phone?
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if the contacts are in gmail, update that one too, or do it 1st & the phone should sync, if the phone is set to sync with pc/mac.