You cannot manage an Elastix server only with Putty
Like an Linux server, you can connect on your server using SSH , username : root, and root password.
Putty is only a tool like WinSCP (SFTP / TFTP client for Windows)
It could be the same or not. But it's not the same usually.
Root password is defined during install in the first step (in same time that HDD part and else)
Admin password is defined during the first boot.