Asus routers would treat it as such because of the the way it generates the config file. But the real problem is the clients (which is what you're actually using). For example the nslookup command in Windows behaves completely different than Ubuntu's. ping and dig also behave differently than nslookup. And there are differences again when using null domains. The list goes on and on... that's why I said "it only leads to confusion"....but would a null domain be considered as a local domain?
On my AX88U I found that nslookup reports "non-existent" for static v4 ips when there is no manual assignment list and it is disabled. Adding or defaulting a DNS server address has no effect, in either case nslookup reports the right DNS. Once I enabled manual assignment and defined my static devices they showed up with the host name defined in the list.
I tried this. I do get the name my router has in its device table for most devices such as my roku, my phone, etc... But other devices like my Canon printer do not return the name from the device list. So i think it may somewhat device specific also.
Have you tried setting a Domain Name on your LAN? It appears you have it blank or have it set to "in-addr.arpa"
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