You mean to say Subject Name, and not Serial Number (because you can't change the ISE serial number ;-)
You have to generate a self signing request on your renamed ISE node and then your internal CA will be alright.
Administration > Certificates > Certificate Signing Requests
Click on Generate CRS - then select "ISE Root CA"
this is not disruptive. It will regenerate the internal CA Root, Node, and Issuing CA certs.