My answer to Why is "mdnsd" draining my battery and how to stop it? explains the role of Android's mDNS Daemon which is an init service, started on demand. It provides Multicast DNS (host/domain name resolution) and DNS-SD (DNS-Based Service Discovery); both part of Zero Configuration Networking.
How to resolve Android's mDNS hostname to IP address?
Technically it's possible for DNS-SD to use the old unicast DNS to resolve the domain name found in the SRV record (of a broadcasted service) to an IP address. But mostly mDNS and DNS-SD are bound to each other. And this is the case with Android.
Android doesn't expose any setting or API to do only the name resolution (as mDNS Responder or Querier) and not the service discovery. Neither the name resolution mechanism uses mDNS. Android's mdnsd serves as mDNS broadcaster / responder only to DNS-SD service. You cannot use either of the both independently (as to my knowledge).
But there are a few options:
Run an app on your Android device with a discoverable service (even a dummy), which uses Android's official API (which in turn interacts with mdnsd underneath) to broadcast and discover services. So any other host on the local network with mDNS/DNS-SD capability can discover the service. For instance use avahi-browse command on a Linux system. Resolving the service provides the IP address of the Android device.
When mdnsd is running, Android device is already broadcasting itself with a hard-coded name: Android.local. If you don't want to broadcast a service, there's another option.
ADB relies on mDNS to discover devices on local network by registering a service of type _adb._tcp (see references here, here and here). So enable "USB Debugging" in Developer Options and you'll see mdnsd running on your device.
Or on a rooted device start mdnsd alone, without starting ADB, by executing setprop ctl.start mdnsd or simply start mdnsd.
In both above cases, when mdnsd is running, executing avahi-resolve-host-name Android.local on a Linux PC should return IP address of your Android device.
What if two Android devices have the same hostname?
In case of name conflict, as the name Android.local is hard-coded, the Android device which joins later automatically renames itself to Android-2.lcoal, Android-3.local and so on (see reference here). So you can resolve the names accordingly.
Any option to change the mDNS hostname?
Coming to the next problem, what if your OEM/ROM developer removed or modified the mdnsd service, or if you want to run with a name of your choice, not the hard-coded one?
Build and run your own more configurable mDNS responder like Avahi on Android device.
Even simpler, patch and rebuild Android's mdnsd to receive a commandline argument for name, or read from a config file if exists.
No, it doesn't need a rooted device. The patched mdnsd binary should run fine from adb shell, or even on a terminal emulator app like Termux. As of this writing, there's only one syscall in mdnsd source code which the seccomp blocks for apps. But it can be removed easily. Neither the DAC or MAC block the execution.