Given the rise of mental health issues and healthcare system limitations, the metaverse emerges as a promising platform for care delivery. Patients and physicians can meet virtually, overcoming constraints of traditional online communication by using avatars. While patient self-reporting is crucial for diagnosis and treatment, little is known about how avatars, core elements of the metaverse, influence communication behavior in such situations. This study explores how avatar identification impacts self-disclosure intention in VR-based mental healthcare, focusing on the roles of self-presence and perceived anonymity. In a lab experiment conducted in Germany using VRChat, 62 participants engaged in simulated one-on-one mental healthcare sessions. Results show that both similarity and wishful identification are significantly associated with self-presence and perceived anonymity. However, only self-presence has a significant positive relationship with self-disclosure intention. These findings advance research on metaverse and telehealth, highlighting the importance of user-avatar dynamics in designing future metaverse mental healthcare interventions.