The psychological profile that structurally documents the case of a depression patient is essential for psychotherapy. Large language models can be applied to summarize the profiles from counseling speech, however, it may suffer from long-context forgetting and produce unverifiable hallucinations, due to overlong length of speech, multi-party interactions and unstructured chatting. Hereby, we propose a StreamProfile, a streaming framework that processes counseling speech incrementally, extracts evidences grounded from ASR transcriptions by storing it in a Hierarchical Evidence Memory, and then performs a Chain-of-Thought pipeline according to PM+ psychological intervention for clinical reasoning. The final profile is synthesized strictly from those evidences, making every claim traceable. Experiments on real-world teenager counseling speech have shown that the proposed StreamProfile system can accurately generate the profiles and prevent hallucination.