Hi @touchkarthick, and welcome to the LE community forum 
CNAME is only a DNS entry.
It helps the client find the IP of the name they are looking for.
That said, once found the IP will have to have a cert for the name they seek.
So, cPanel will have to respond to HTTPS://example.mywebsite.com securely.
That means the cert will have to contain that new FQDN.