Is it required to have the same Domain Name and Common Name for SSL Certificate?

The domain of the URL must match the subject of the certificate. In former times this could be either by setting the domain as CN of the certificate or by having the domain set as a subject alternative name. Support for CN was deprecated for a long time (at least 17 years, see RFC 2818) and Chrome browser will not even look at the CN anymore so today you need to have the domain of the URL as a subject alternative name. Note that there can be multiple subject alternative names and thus the certificate can be used for multiple domains.

Your web browser will require the host name in the URL to match what is in the certificate.

It should check first the alternate subject name list (if the extension is present) to see if any of the entries matche or, if there is no SAN extension, the subject's common name field.