computer name keeps changing

Hello, I am having what I think is a fairly common problem but for which I have found no satisfactory solution. I am baffled that OS-X has such a problem.

Basically I work at an office where, while sitting at my desk I have a wired ethernet-connection (through a USB-C docking station, to which I also connect my displays and other stuff), but when I get up to go to meetings etc I wanna use WiFi.

The problem is that, if I keep my WiFi on, while I am connected to the wired network my computer's name keeps changing. I have verified 100% this only happens when both wired and WiFi are connected.

I suspect this happens because my machine has two valid connections and probably sees another machine (which is really the same machine through the other network) with the same name, I even get a pop-up saying so every once in a while. Here is a screenshot of my computer-name from Settings->Sharing the red part is my last name, I am sure it is unique within my network

Why do I care? well, this is what I get when I try to resolve my hostname from another machine (Ubuntu 22.04) in that same network:

me@ubuntu-machine:~$ nslookup <my-last-name>-mac.<company-domain>
Server:		127.0.0.53
Address:	127.0.0.53#53

** server can't find <my-last-name>-mac.<company-domain>: NXDOMAIN

me@ubuntu-machine:~$ nslookup <my-last-name>-mac-571.<company-domain>
Server:		127.0.0.53
Address:	127.0.0.53#53

Non-authoritative answer:
Name:	<my-last-name>-mac-571.<company-domain>
Address: 10.34.24.93

So as you can see, this is not just some weird computer name used for apple-only stuff, it is the actual hostname which is advertised...

The obvious solution is to turn wifi on/off each time I plug/unplug my machine, but I refuse to accept that there is no better option, specially since having WiFi on can be necessary even when connected to the wired network to use AirDrop from my phone or to/from other machines.

I have tried turning off all sharing options (as you can see in the screenshot), turning off "Find my Mac" (suggested by some threads) but still no luck. Also arranged the "Service Order" of my connections under Settings->Network to try and have WiFi only used when it's the only option but it made no difference:

Is there really no way to have OS-X be smart enough to realize that other machine it is seeing is really the same machine?