The entire premise of this question seems flawed. I will try and answer the question you asked, rather than theorize what your trying to accomplish.
Obviously If this is for Private IPs, your defining something which exists on a LAN. Dynamic DNS is not for such uses, it only places a domain on an externally facing network. It's something you might want on your router, to create a 'static domain' to workaround an ISP constantly changing your public IP address.
You interestingly lack the ability to set a static IP address, which is the sanest way to deal with problems regarding changing IPs. Often a router will automatically report an A record, when it's DNS queried for specific hostname. I recommend you verify your hostname is set correctly, and connecting in said manner is not possible, before venturing further.
MDNS is your last, and likely only, option to such a problem. Remember other devices must have the ability to multicast, and use MDNS addresses. Setting this up is beyond the scope of this answer, as it's specific to each OS. Mac OS X calls this service Bonjour, It's also available for Windows and is installed with iTunes. Gnu/Linux provides MDNS via Avahi, which is often pre-installed with most recent GNU/Linux distributions.
You wanted an answer to your question, and now you got one. Please check accept, It keeps this whole shebang running.