Hi,
I recommend you use a certificate from a trusted public authority such as GeoTrust, Thawte, DigiCert, Comodo, GoDaddy, etc., unless all devices are domain-joined and are configured to automatically trust certificates from your internal CA. Please note
that some device types are not able to be joined to your domain.
Regardless of whether or not you are using public CA or internal CA, please make a
new certificate request using the appropriate subject name. One method (there are others) for this would be to use the wizard in IIS Manager.
-TP