In my cPanel I generated a CSR for an SSL. I then went through the GeoTrust Radip SSL form on The Planet and purchased a certificate. Now when someone goes to my site they get a domain name mis-match. Orders for my domain go through www.modernhq.com but the certificate is for modernhq.com.

I went into cPanel to see if I could configure it and I can not. I talked to Tech Support and they said I have to regenerate a CSR with the www. prefix but I can not do that in cPanel. What can I do?

NORAMLLY people will create a subdoamin such as secure.mydomain.com and get the CSR for that. Get the certificate and install it and then you can https://secure.mydomain.com and all will be well in the real world.

That's because when you went to generate the csr, you entered modernhq.com instead of www.modernhq.com
Just generate a new csr and submit it, to re-issue the cert.