Verizon owns the router and the configuration, presumably, even though you're allowed to change it. This seems perfectly legitimate to me, particularly given how tech-incompetent most of their customers are. Only real concern is security, but it's a minimal one. (Remember back in the day when you could figure out the default passwords for Verizon routers by SSID alone?)

If this concerns you, roll your own access point (you probably have anyway if you're reading this).