The router transmits the old network name within a few seconds after I changed it. What I've done:
wifi down uci set wireless.@wifi-iface[0].ssid=NEW_SSID uci commit wireless wifi up
After that, in the available networks, I see the old network and the new one for a few seconds. Why is this happening and, most importantly, how to fix it?
Client devices show entries in their list of available stations for a bit even after they are gone, for several reasons.
Firstly, it takes a few seconds to scan through the wifi bands to get a list of stations (usually between 3 and 5 seconds, depending on wifi hardware). Secondly, they would not remove a station from the list until it has been gone for several consecutive scan cycles. Likewise, they would not add a network to the list until it has shown in a few scan cycles. This is simple hysteresis to prevent the list of network from fluctuating wildly every few seconds.
This is completely regular behaviour, there is nothing to fix.
It is important to note that everything happens after turning on the network. It doesn't matter how long I wait in the web interface, changes will only be available after turning on the network.