I don't believe it will let you keep the name the same, it will give you an error the name already exists, do you want to overwrite.
You could do an instant recovery, I usually name it servername_ir. Then I don't connect it to any networks. Once the server is powered on, I login and get whatever files I need or backups from SQL. Then you can change the IP to a static, connect it to your production network or an isolated network, and connect to the Server, grad the files, then stop publishing the instant recovery.
Just how I might attempt the recovery.