How to set up dynamic DNS for 'host' in isc dhcpd

Question

I have set up a couple of subnets in my network, and in one of these subnets I'm setting up hosts like this:

subnet 10.0.0.0 netmask 255.255.255.0 {
    option ntp-servers 10.0.0.1;
    option time-servers 10.0.0.1;
    authoritative;
    allow client-updates;
    allow unknown-clients;
    range 10.0.0.10 10.0.0.250;
    option domain-name-servers 10.0.0.1;
    ddns-updates on;
    ddns-domainname "yellow";
    option domain-search "yellow";
    
    # Rack 3 UPS
    host rack3ups {
      allow client-updates;
        hardware ethernet 28:29:86:xxxxxxxx;
        fixed-address 10.0.0.203;
        }

The clients that are just in the subnet update the bind dns server, and I can see them in the leases file, but not the host definitions.

Can someone enlighten me why this is not working, or maybe this should not work and I should update the dns server myself (which feels like overkill).

Thanks, Henk