The primary cause of this visibility is the architecture of the Short Message Service (SMS). Unlike a phone call, which can be initiated as an anonymous request to the network, a text message requires a sender address to ensure the recipient's device knows where to send the reply. Consequently, simply changing a system-level setting on your device does not strip the number from the packet of data sent to the cellular tower.
Useful Library identifies that this transparency often leads to unwanted exposure in professional or personal scenarios. To truly obscure your identity, you must move beyond native dialer settings and utilize secondary routing methods or third-party interfaces that decouple your personal SIM card from the message transmission.