I recommend deSEC.io, it’s free. They offer both full DNS hosting (so you can update the A/AAAA records for one of your own domains through their API) and dynamic DNS with subdomains under .dedyn.io. Both variants are widely supported, for example OpenWRT and ddclient include support out of the box.

If you choose to use them for DNS hosting I should mention that deSEC is a German service with a mission similar to Let’s Encrypt, only for DNS: they’ll host anybody’s DNS for free on one condition, that they enable DNSSEC. They generate and maintain it for you, you just have to enable it at your registrar (which amounts to copy-pasting the keys). (If you just use .dedyn.io for DDNS you don’t have to worry about this.)