Well, some new information now available.
1. I found a advice on the forum that you should use SSH to make it work. I edited the /etc/config/system file and succeeded to change the displayed hostname and router name. (actually the file where the names were was not /etc/config/dhcp as in the hint).
2. But after I connected the network those changes were gone and defaukts were in place.
3. I updated the firmware. Now I was able to change those values even through the local console.
It seems that this is issue with firmware version or there is some reason why you need to be online to make the change stay?