From the documentation:
If you use DHCP instead of a static IP address for the vCenter Server Appliance or Platform Services Controller appliance, verify that the appliance name is updated in the domain name service (DNS). If you can ping the appliance name, the name is updated in DNS.
It depends on the DHCP server, i.e. it's configuration, whether it creates/updates DNS records. You will have to check if this works with your router.
That said, consider to setup vCSA with a static IP address, or make at least sure that you create a reservation in the DHCP server, so that the vCSA's IP address always remains the same.
André