In which protocol does router use to advertise itself and the network(including the name of the netwrok, like hotspot)? I haven't found it on the interent, do you have any ideas?
If you refer to Wireless APs, they advertise themselves using the IEEE 802.11 standard. Particularly, beacon frames are used. You can check these frames on Wireshark captures: https://wiki.wireshark.org/SampleCaptures#Wifi_.2F_Wireless_LAN_captures_.2F_802.11
On the other hand, if you mean over the wire, as you have been already told, they do not advertise their name. In IPv6 there is the NDP protocol which advertises routers, but not their names. However, you can use reverse DNS query to obtain the DNS name of a router, so maybe you refer to that.