I have done this before but I always keep the same name an IP so that I don't have to reconnect each ESXi host and my vSphere Client users don't have to use a different name.
What I do in this scenario is build the new server with a temp name/IP.
Backup the vCenter DB and SSL certs (this is very important).
Power down the old vCenter.
Re-IP/Re-Name the new to match the old.
Copy the SSL certs to the proper location (C:\ProgramData\VMware\VMware VirtualCenter\SSL)
Create your DSN and install vCenter using the old DB. The DB will be upgraded.
Your hosts will automatically connect to the new server.