You cannot edit the Name directly, because the Name of the TermStore is simply the name of the MetadataWebServiceApplicationProxy.
So what you have to do is to rename that one instead. In your example, you have to get the SPMetadataServiceApplication first, find the right proxy and rename it. This should look like this, assumed that your SPMetadataServiceApplication is named "Managed Metadata Service Application"
$metadataApplication = Get-SPMetadataServiceApplication -Identity "Managed Metadata Service Application"
foreach($proxy in $metadataApplication.ServiceApplicationProxyGroup.Proxies)
{
if($proxy.Name -like "*Managed Metadata Service Application*")
{
$proxy.Name = "Managed Metadata Service"
$proxy.Update()
}
}
or short version
$metadataApplication = Get-SPMetadataServiceApplication -Identity "Managed Metadata Service Application"
$proxy = $metadataApplication.ServiceApplicationProxyGroup.Proxies | Where-Object { $_.Name -like "*Managed Metadata Service Application*" }
$proxy.Name = "Managed Metadata Service";
$proxy.Update();