$_.Name will reference the public folder name. If you need the mailbox name...
Get-Mailbox | ForEach-Object {
$Mailbox = $_
Get-PublicFolder -Recurse | ForEach-Object {
Add-PublicFolderClientPermission -Identity $_.name -AccessRights None -User $Mailbox.DistinguishedName
}
}
Is that what you're after? Seems like it will catch a bit too much (adds everyone to every public folder).
Chris