Own domain without fixed IP

Although some information is missing in your question, such as how you have configured the service in your domain manager and the configuration of the ekain service (less relevant for this case), I think your problem is that in the manager of your domain you have configured the option "redirect" and send it to ekain and there you tell him what to do with your domain.

If my assumption is correct, that is the reason that the domain of the addressed destination comes out. For your suspekain.eus domain to work correctly on the internet you must configure the DNS service of your domain manager and define the access points (ns) provided by ekain.dickdns.org (if they exist).

This will allow the resolution of the IP for your domain to be made transparently, which is the IP of your raspberry that knows ekain and that is your domain that is seen in the browser.