Where is that DHCP server? Are you sure they get actual DHCP leases?
Typically Docker’s internal resolution is basically just injecting the hostnames in /etc/hosts, but Docker also supports macvlan and macvtap networks too which can expose a container network directly on the network.
But I think 99% of containers just use the default bridge network. I never heard of a Docker container running a DHCP client, most containers run the app process directly and don’t do a full boot.