It is really simple, in order to be able to use SecureLine you need to connect to a ISP/access point first.
No Internet connection = no way to use a VPN
You are traveling and your laptop is trying to use the nearest and/or strongest signal that is around.
e.g.
If you are in a large(r) city, it connects to access point A.
When you move to the other side of the city (or to another city) the signal will get to weak and eventually entirely lost.
Your laptop searches for a new access point and will find access point B the best one to connect to.
So yes, you are constantly changing networks and the firewall is detecting that and is asking you what to do.
Perfectly normal.
I’m thinking computerguy.bry said he saw the same network name in two places: Atlanta GA and Lima, Peru
I have a new laptop with Avast Premier and VPN. I'm traveling and have seen this same new network pop up in Atlanta, Ga and now in Lima, Peru.
It says Local name: DESKTOP-LIE1NEK [fe80::4c6c:cc11:ade7:8a3b]
He also says he is using Avast Secureline VPN. Since a VPN spoofs the real IP connection maybe he is seeing avast spoofing the US connection when connected in Peru?
Guessing as the original post is a little unclear as to what the original network name in the US was and the new one in Peru.
BTW, a network will have any possible name assigned to it by the owner of that network. As Rednose says, use Public setting for Public Wi-Fi networks.