What router can accept the Internet with one SSID (or bridge) and already distribute his network with his SSID?
Answer
Hello! This feature is available on many routers. The best mode for such a connection is bridge mode.
But when connecting two routers via Wi-Fi network, the connection speed may drop significantly. And the stability of the Wi-Fi network may not be very good. In your case, if possible, it is better to lay a network cable between the routers. Then everything will definitely work without problems. Well, if there is no such possibility, you can choose a router that can connect to another router via Wi-Fi and give out its network with a different SSID and password.
Almost all TP-Link routers have a bridge mode (WDS) – /tp-link/tp-link-router-setting-in-bridge-mode-wds-we-connect-two-wi-fi-fi-routers/
On D-LINK routers there is such an option (but as far as I understand, not on all models and firmware) – /d-link/client-mode-bridge-and-repiter-on-the-d-link-router/
Netis and Zyxel Keenetic have this feature on them as well. Probably not on all models. There are many variants.