Is your DHCP also going to be provisioning the gateway address? If it is you'll need to do two things:
Set-NetIPInterface -InterfaceAlias 'Ethernet 1' -Dhcp Enabled
and:
Get-NetIPAddress -InterfaceAlias 'Ethernet 1' | Remove-NetRoute
Also, knowing just the name of the machine isn't enough. You'll also have to provide the name of the NIC you want to change, and that may be different on each machine.
When you change the IP address you're going to be disconnected, so build that problem into the script you write.