Will this automatically change all of the VMs using the port groups under that DSV or will I have to change all of my VMs networking to use the new DSV name?
You can change the VDS name at any time, there is no impact or further work required. You will not have to modify any of the virtual machine network connections or port groups.
You might want to also change the Uplinks name, as it typically is in the format of "VDSName-DVUplinks-##"