Free DNS?

[LoadWB]

dyndns works just fine, and iirc there's an Amiga program for it - though most routers these days support dynamic DNS.

I wrote an ARexx script a while back (1999) which I suspect is either still compatible or can be made compatible.  DynDNS does still offer the free service, but you are required to sign up for a 30 day trial of Pro, first.  Sad end of an era.

[LoadWB]

From the site:
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When the trial ends

 After the 14 day trial, you will be charged our low yearly fee of  just $20 a year (or sign up for five years and get 10% off!) to keep  your DynDNS Pro service. Only valid major credit cards (not PayPal) are  accepted for DynDNS Pro trials.
 Decide you no longer want the DynDNS Pro trial? Just cancel your  DynDNS Pro trial within 14 days and you will not be charged. You may  keep one hostname free of charge for trying out the DynDNS Pro trial.

So, sign up then cancel is what it sounds like.  DynDNS has the name recognition which will benefit them, but there are a massive number of services out there.  Having said that, there are also a lot of firmwares for routers and modems which support nothing but DynDNS or only a few others like TZO.  (And TZO ain't free.)