Peer feedback can enhance learning but may introduce issues like peer pressure and distrust, particularly with professional competencies like teamwork. This jeopardizes the feedback process and skill development crucial for undergraduate students' career preparation. To address this, two approaches are generally used: anonymizing feedback or incorporating feedback dialogue. However, the impact of anonymity on trust and safety is unclear due to a loss of dialogue. Additionally, the effect of feedback dialogue in the context of competencies remains largely unexplored. Employing a mixed-methods approach, we divided sixty-three participants into an experimental group receiving identifiable online peer feedback with dialogue and a control group receiving anonymous feedback only. We measured students' psychological safety and trust in giving feedback on teamwork competencies, feedback quality and perceptions of the feedback process. Quantitative results showed no significant differences in safety and trust perceptions between groups, indicating that anonymity and feedback dialogue contribute to a comparably safe environment. However, the qualitative results indicated that the experimental group held more positive attitudes toward the feedback process and their feedback seemed more nuanced. This suggests that dialogue-enhanced peer feedback is preferred for fostering a safe and effective peer feedback exchange that supports professional competency development.