There are 2 different ways to use the "repeater" connection. Both have their own limitations as (hidden) travel router.
"Repeater" is only 1/2 of the information, the other half is "Network Mode"
- Router
The hotel sees 1 and only 1 device connected. That device shows its MAC address, its DHCP-client-name and gets 1 IP address.
However ... received packets with TTL=1 will NOT pass the router. (eg portal page) . Hotel may deny access for any MAC of some router vendor (first 6 hex numbers of MAC). Hotel might receive packets with varying TTL values, and refuse further access. (Most mobile networks do this trick, if the subscription is for the smartphone only) Even the DHCP-client-name if not changed is an alert for the hotel (GL.inet router name).
- Extender
The hotel sees only one MAC address (the MAC address of the router) in the packet headers. The MAC address of the client device will be in the DHCP requests, with a different MAC address in its header. Each client device needs another IP address.
However .... the DHCP server could limit the number of IP addresses to 1 per MAC address (this is sometimes just the DHCP default setting). The client may not be reachable (if the AP uses the clients MAC address and not the router MAC address in the packet header.) Some AP vendors have merged the ARP and DHCP "MAC-IP table". They are 99% identical, but not when an extender is used. That's why DHCP behind an extender often fails.
Self assigned similar or copied IP addresses may not work. If the ARP-table in the host AP/router is set to "listen only", it doesn't send ARP requests and refuses to use the client ARP responses. Only the local DHCP server will update the ARP table.