Scenario: You need to change the TLSCertificateName for the send connector because you recently upgraded your certificate. (Get-sendconnector | Select Name, TLSCertificateName)
Solution: Perform the following steps:
#Pull the Cert Info into a Variable:
$TLSCert = Get-ExchangeCertificate -Thumbprint <Thumbprint> -server <Servername>
#Format the CertName so it an acceptable value for the TLSCertificateName property
$TLSCertName = “<I>$($TLSCert.Issuer)<S>$($TLSCert.Subject)”
#Set the TLSCertificateName for the send connector:
Set-SendConnector <Name of send connector> -TLSCertificateName $TLSCertName