Using Cyanogenmod 11 with Android 4.x or running the general pre-installed mobile Android image, this worked without problems:
Use DHCP reservation feature of your server and maybe give it a DNS A hostname so you are able to access (at least ping) your mobile phone via a constant name/IP in your local network.
But starting with CM12 and Android 5.x, your phone gets a new MAC address or DHCP ID on every reboot, or even every time you reconnect to your WLAN.
A MAC address is definitely not wanted to be changed ever. So this results e.g. in many useless IP lease entries in your DHCP server, and your mapped DNS names may not work any more.
Cyanogenmod developers seem to ignore this problem as seen on these threads:
The first thread is closed because of „too old“ with the suggestion of creating a new thread, the second one is closed because of „duplicate“ – which is quite contradictory.
For me the only workaround at this moment was to set a static IP address for the WLAN connection on my phone.