At the moment, tawk.to does not have a built-in feature that automatically performs phone-number or email lookups against third-party databases such as Google, Facebook, or other data-enrichment services.
That said, this is a useful feature request, and I’ll make sure your feedback is passed along to our product team for consideration. The feasibility would also depend on the APIs, permissions, privacy requirements, and data-access policies of the external services involved.