When I had DSL, I bought my own modem and connected it to the same router I used at a previous place. They when to charge ~$10/month, so I spent about $20 and got a basic modem.
My current internet is Ethernet at the wall, so no need for a modem, and AFAIK the company doesn’t even provide routers (didn’t ask, I just used the one I had). All I needed was the gateway, netmask, and our static (CGNATed) IP. They wrote that in a piece of paper, which I keep in my safe so I don’t need to call them just because I reset my router or something.
I think they know who I am by now because I call pretty much every time the Internet goes out. It’s a small company (only serves my town of 30-40k people), and I’m probably the only one with a ln enterprise-y router (Mikrotik) with a separate AP (Ubiquiti). Yet I still need to do the basic troubleshooting before they’ll actually look into the traffic on their end.