Suppose we know the Thumbprint of the certificate then we can use the below command to update or change the certificate's friendly name.
$cert = Get-ChildItem ` -Path Cert:\LocalMachine\My\43E6035D120EBE9ECE8100E8F38B85A9F1C1140F
$cert.FriendlyName = "mysitecert"
The above command will update the certificate-friendly name to "mysitecert". If you don't know the thumbprint or how to retrieve it, you can use different properties like Subject name, friendly name, etc.
$cert = Get-ChildItem -path ` Cert:\LocalMachine\My\` | where{$_.Subject -eq "CN=mysite.local"}
$cert.FriendlyName = "mysitecert"