There are organizational interactions where the confidentiality of the customer is to be maintained and guaranteed. The anonymity of the customer may either facilitate in boosting customer experience or company productivity.
It might sound confusing, but let us take two examples. For instance, a customer wishes to register a complaint and wishes to remain anonymous, or, if a business is an intermediary between two parties, and exchanging real information ( contact information) between these parties may compromise the survival of the intermediary. There are many ecommerce platforms that brings together resellers( vendors) and customers, that have implemented this feature. This feature protects them from losing their customers.
Probably the second example may fall way far from the first, but you get the picture. There will be instances where some information of the customers should not be disclosed. And there are contact center softwares that provides such features as call patching, virtual number, etc.
Identify whether your business requires such non-disclosures and if you do, immediately invest on such features that protects your customer base.