I agree that it very much depends. I think this is true for all network anonymity features. E.g. changing MAC address on every connect is probably a good precaution for hotel and train networks, but not for corporate or home ones.
Looks like in network-manager that at least can be set on a connection basis with the mac-address-randomization option.
Apparently there is a per-connection option for this, as well, ipv4.dhcp-hostname! (and a ipv6 equivalent if you care about that) I think that would address your issue, as the wired and wireless connection are considered separate connections: Customizing dhcp client hostname in network-manager - #2 by MisterNo - Network - Linux Tips
Assuming you’re using nm, of course 