Don't know if still needed and applicable, but here a more detailed solution that worked for us. My mother-in-law's phone (also Verizon, but a Motorola) also drove us nuts with these notifications, the phone relentlessly telling her she was roaming whenever she connected to another carrier than Verizon (which does happen a lot when she visits us in Germany 
).
Possible solutions were:
- turn roaming off
Would leave her here (and anybody beyond the reach of "their" carrier) without contact to the outer world. No alternative for us. - set phone to flight mode
No calls, texts, etc. would come through, either. Rather pointless (unless you enjoy taking off the communicative shackle, which is nice every once in a while) - turn phone off
Effect the same as setting it to flight mode. - turn phone to "silent"
You still see what came in when you check your screen, but again, you won't hear calls coming in. - SOLVED our problem (on the Motorola, but I'm sure other brands work similar): turn off roaming notification (after finally finding it...)
1. Go to "Settings"
2. Tap "Apps & Notifications"
3. Tap "Notifications"
4. Tap "Notifications" (yes, again, it's a new point, on her phone with a bell next to it)
5. Tap the three little dots at the top-right corner of the next screen
6. Tap "Show system" in the little menu that drops down then
7. Scroll way down to the entries called "Phone" (there are three of them on her phone)
8. Tap the third "Phone" entry (on her phone, it has a generic android icon next to it, not a telephone handset)
9. There you'll see "Verizon Roaming Status", but the switch will be grayed out (can't change it)
10. Instead tap the words "Verizon Roaming Status"
11. Tap "Importance"
12. Set it to "Medium" (=no sound anymore, but you'll still see the icon, a triangle in her case, in the status bar indicating that you're roaming) or "Low" (=you won't be notified at all when you're roaming)...we chose "Medium" and enjoyed the ensuing silence.
Did the trick for us and restored sanity. Hope it helps!
