First, If you are looking for (1) a free domain name with (2) the
capability to automatically update the dns record whenever the IP
address of a host changes, such as the dyndns free service previously
did, then I wonder if it may be possible to
1. use a free domain name from here:
http://www.dot.tk/en/index.html?lang=en
which is managed by Freenom, who also have 3 other TLDs to select from:
http://www.freenom.com/en/freeandpaiddomains.html
and
2. if you are good with scripts, whether it may also be possible to
use a script to update the dns records in either
(a) the DNS servers managed by Freenom for you domain, or
(b) some DNS servers managed by yourself (though I am not sure you
could run a DNS server on an IP that itself may be dynamically changing)
When I looked last at .tk (when dyndns stopped being free) I could not
see how to update the dns records dynamically from my own host, but
there may be some better guidance around, these days.