Some years ago I had trouble with maintaining a connection to Verizon on the Fire Department laptop as I went yo my came in northern Vermont. What I didn't know, and now I do from my trip is that both Verizon and AT&T have coverage gaps handled by other carriers that are not their network. When you are in one of these spots you can make and keep phone calls as well as text but you can't use data or you are limited to some very small amount of data.
I ran into this problem on my trip when my niece Brianna was with me and we were at the Grand Canyon. My phone had a hard time downloading data. My phone said AT&T and I got a text message from AT&T saying I reached my limit for data for being out of network. My phone still said AT&T so I kept downloading. I then got a text from AT&T saying that I would be shut off if I kept using data and that they would charge me for more usage than out of network allows. They shut off my data and downloaded something to my phone to change AT&T to out of network. Thsts right they changed what I see to out of network after it said AT&T.
They allowed me to make and perceive phone calls and text but no web surfing or downloads. With this change to my phone, when I drive through Troy, NH my phone switches to out of network and back to AT&T when I get to Swansea, NH.
So, when you view either Verizon or AT&T's coverage maps the map doesn't show all their networks, and for the partner networks that you can't see, you do not have all the benefits of your home plan even though you are in the USA.
Since they changed my phone I now see out of network where you all still see your carrier name.
They didn't charge me extra and I think for good reason as if it says AT&T then I should expect the service I pay for.
Now I know why Verizon data didn't work in some areas on my way to Vermont.