Thank you very much for your detailed answer.
I was not aware until now that mDNS in Hyperion is also used for other purposes besides basic name resolution. With this it is also completely understandable that you don't want to make any fundamental changes just to support my probably quite rare legacy environment.
Of course it is always a fallback option to work with DHCP reservations and thus pseudo-static IP addresses or DNS aliases. It just unfortunately further increases the maintenance overhead, which is why I was hoping for a simple solution directly in Hyperion.
On Github I have seen that the use of mDNS is determined by the identifier ENABLE_MDNS at the crucial points for name resolution. Would Hyperion work if I recompile it without ENABLE_MDNS defined?