Yes, you can do that using the External Contacts feature.
With a PureCloud 3 license, you can create and maintain a contact database and view your omnichannel interaction history with those contacts. With the lower-level PureCloud 1 and 2 licenses, you cannot view and track interaction history, but you can still create and maintain the contact database, and agents will receive native screen pops containing the customer information upon receiving interactions.
In addition, contact information can be maintained in several ways:
* agents can enter it while handling interactions
* users can enter it it from the web interface
* admins can upload it in a CSV
* admins can sync it from Salesforce
For more information, see:
https://help.mypurecloud.com/articles/about-external-contacts/