networking

Uninitiated noon question below.

A couple of days ago, this haprogram https://programming.dev/post/41491279

Now, during the phonecall with my ISP, the guy asked, "is your router an ASUS?" to which I answered, "yes and no, because it's sold as a router but I have it in AP mode and my actual router is OpenWrt on a Raspberry Pi." To which he replied "noice!"

How did he know the make of my access point? A few of my own thoughts are:

1. he was referring to historical data (I've been a loyal customer of theirs for a looong time...) from a time when I was using the same topology (setup?) but without a VPN on the router, so the hostname of the AP (stored in /etc/hostname on the ASUS OS/firmware ?) was simply displayed on whatever software an ISP uses for troubleshooting through... an ARP? But aren't ARPs limited to a LAN/they cannot resolve beyond a hop? Or perhaps a variant of DNS? How indeed do hostnames transmit? Are they in the IP header by default?
2. as in 1 above, but he actively used nmap or some other recog program
3. as in 1 above but from a time when I was in fact using the ASUS machine as a router
4. my VPN is "leaking" - not likely, because all my traffic either goes through the wireguard interface on OpenWrt/RPi, or it doesn't go anywhere...

If 1, 2 or 3: why do they keep historical data on me? Is it praxis?