Caller identification (or Caller ID) is a telephone service that transmits a caller’s phone number to a receiving party’s telephony equipment when the call is being set up. Besides the telephone number, the Caller ID service may transmit a name associated with the calling telephone number. The appearance of the first Caller ID devices caused suspicion among the users and the public because of the potential security and privacy issues that the caller identification may cause. Privacy issues apply to users of the Caller ID applications, but also to non-users whose phone numbers are stored in the database of some Caller ID application. The emergence of the data privacy laws has led discussions on the privacy policies of Caller ID applications and their compliance with the law. In this paper we investigate two Caller ID applications, Truecaller and Everybody, and compliance of their privacy policies with the data privacy laws, especially the GDPR, the ePrivacy Directive and the ePrivacy Regulation. Further, we deal in more detail with the data privacy problem of non-users and we give the connection between those problems, and the inverse privacy problem. In order to solve the privacy problem of non-users, we develop the mathematical model based on the notions of privacy variables and sensitivity function. Finally, we discussed open questions related to the identity protection of Caller ID app users and non-users, and their trust in Caller ID apps.