I see that except public key mostly everything else changes after the certificate renewal; should I reconfigure the programs/softwares to use the renewed certificate? if there is 'something' that stays the same after the renewal, I can use 'that something' to identify the certificate. can any one help me here?
Most software, particularly web browsers use the Common Name, and Subject Alternate Name fields to ensure the certificate is valid for a site.
If the identified (be it IP address or hostname - whichever is used to access the site) aligns with a CN or SAN and the certificate otherwise passes validation (accepted certificate authority, start and end dates, etc) then that certificate is considered valid.
Most likely this is mandated by the RFC, but I'm not particularly familiar with that, so I'm speaking only from observation - not with any authority.
Note that this is a massive oversimplification, HSTS and certificate pinning often play a role these days too, which can make an otherwise valid certificate invalid.