I don't think they are "advertising" on that portion of the lockscreen - it's simply identifying the network you're on. If you put in a Fi SIM card, it would probably say Fi or Project Fi at the top left.
As for the huge splash you say was on your Samsung on boot, that's carrier branded handsets for you. Unlocked and non-branded phones won't have that.
I wonder if something changed when I updated the "My Verizon" app yesterday
I've never understood the carrier logos/branding on the screen. I know who my carrier is, and only I use my phone, so they're not advertizing to anyone. Even if someone was looking over my shoulder, it's only on the lock screen, so who's going to see it?
I think maybe they just get into this habit of branding everything, and no one stops to think whether it's even worth doing.
Oh well. Mine says "Verizon Wireless" in small text at the top. It could be worse. A lot worse. My S5 used to have a huge Verizon splash screen on boot. Also pointless.
If you happened to roam to another network it would identify it there as well.
My Always On Display! My phone battery last all day.
Yes. It is called Glance Plus in the App Store.How'd you get that working? Is it an app?