When I generated the original certificate, I specified an incorrect common name.  Can you change it to the correct common name?

The name of the site is specified within the certificate in the "Issued to" field. This must match whatever is being displayed in the address bar.  The "common name" of the certificate cannot be changed without invalidating the certificate.  The only course of action would be for you to generate a new Certificate Signing Request (CSR), this time specifying the correct common name, and then to purchase a new certificate.