Migrate the server from 2008 to 2016: keep the same host name and IP

I have a server, DHCP1 that runs on Windows Server 2008 and I want to migrate it to Windows Server 2016 with no downtime to the DHCP service.

My problem is that I have to keep the same host names and IP addresses for the 2016 server. So I will have to deactivate the 2008 server, replace it with a 2016 server and import all the configuration that I exported from the 2008 server.

During this migration, how does my client know which server will connect to? On what basis, my client will determine if he has connected to the Windows 2008 server or the Windows 2016 server, since both servers have the same IP address and the same hostname.