The growing use of multimedia applications in digital health (eHealth) has highlighted the need for secure communication protocols to protect sensitive patient data. Security is expected as a crucial requirement also of future sixth-generation (6G) networks, which represent a valuable means to favor the definitive development of eHealth, hitherto hindered by the insufficient adequacy of technologies. In particular, device-to-device (D2D) has already emerged in previous generations of cellular networks as a promising solution to enable fast and reliable data exchange between devices, and it is expected to be an enabling technology of forthcoming 6G networks as well. However, the security of D2D communication in eHealth is a major concern due to the possibility of unauthorized access and data breaches. To address these challenges, this paper proposes an authentication protocol to secure D2D communications established to support the development of eHealth multimedia applications in 6G-oriented networks. The conducted performance evaluation demonstrates the effectiveness of the proposed protocol in achieving secure and reliable D2D communications and shows the benefits offered by the proposed solution in terms of energy savings.