What parameter in an Invite determines the channel Asterisk tries to find a match for?

What header in an incoming invite contains the information that Asterisk uses to determine the identity of the incoming call by trying to find a match in its channel configuration file sip.conf or pjsip.conf?

That depends on the configuration. The user portion of the ‘From’ header can be used to do a match, there is also a configuration option to match based on the username in the authentication header, you can also configure chan_pjsip to match based on an explicit header, and you can also just not do matching based on any contents of the message and do it based on the source IP address.