The behavior of the search based screen pop is governed by the "softphone settings" configuration within Salesforce. You can configure exactly how you want the OpenCTI phone to behave in the event of no match, one match, or multiple matches; you can also create multiple softphones and assign them individually or as a group to various users throughout your organization.
The default behavior of the Genesys Cloud for Salesforce OpenCTI softphone is to use the ANI as the sf_SearchValue. This value can be overridden with either a new search value, or with the sf_URLPop attribute, which can direct you either to a specific Salesforce page (like a visualforce page), or to a specific Salesforce object by that object's ID. The behavior of screen pops and the associated attributes is documented here:
https://help.mypurecloud.com/articles/screen-pop-in-genesys-cloud-for-salesforce/ (there's also a link to the Salesforce documentation regarding the softphone settings on this page).
In addition to these default controls, there are client extension points, which allow you to further customize screen pop behaviors using your own Apex code. This could allow you to vary the screen pop behavior in a more situational fashion (i.e. perform a screen pop under condition A, but not under condition B). Extension points are documented here:
https://help.mypurecloud.com/articles/extension-points-in-genesys-cloud-for-salesforce/------------------------------
Richard Schott
Genesys - Employees
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