I have registered an account at vimexx.nl and created a cheap domain name (1.56€ for the first year).
Then I have changed the nameservers to the 3 name servers of digital ocean:
ns2.digitalocean.comns3.digitalocean.comns1.digitalocean.com
Note that this takes quite some time before they are effectively used.
I have registered an account at DigitalOcean
Under Networking I added the domain I have registered above at Vimexx.nl.
For that domain I have manually created an A record with
Hostname = @will direct to =the public IP address of my bbox modem
It takes some time before the above changes appear to be working. On mac OS it might be needed to clear the local DNS cache to speed it up: