How about looking into ddns-scripts package and its LuCI interface luci-app-ddns ...
if you really mean "custom" DDNS service, you might edit the DDNS service provider list in ddns-scripts after installation and add your specific site there.
Note that the default list of DDNS providers in that package is already rather large, so hopefully your site is already found there: https://github.com/openwrt/packages/blob/master/net/ddns-scripts/files/services