This is related to Backup Assistant Plus. You can sign into your MyVerizon account online and remove the feature from your account. Additionally there have dozens of similar posts on this community, a search for "VZWNMN" would have found most of them. Those discussions will have more information on this subject.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
Ok, I was getting those same messages. After hours of web searching and spending some time with a tech person here is the solution that seemed to work out for me. I have a Motorola razr m.
1. Go to Settings, Storage (in the device section), Apps, under the all section I disabled the backup assistant. I also disabled Email. Once I disabled that I hit clear data. This clears out your alternate email addresses. If you want an alt email go to the store and download that specific app after completing this.
2. After those are disabled in the same area (settings, storage, apps, under the all section) go to Gmail and hit clear data than ok.
3. Now hit the home button and get into your apps. (it's the center bottom button looks like a circle with little squares in it. Than hit Gmail. When it opens you get an account not synced message with two options Sync now or Change Sync Settings: hit the Change Sync Settings and uncheck Auto-sync app data. now click Sync Now. When your email opens you should see a message saying Auto-sync is off in the mail box. Hit the X to close it.
Since doing that I haven't received that stupid message. Hope this helps you out.