We propose DarkStream, a streaming speech synthesis model for real-time speaker anonymization. To improve content encoding under strict latency constraints, DarkStream combines a causal waveform encoder, a short lookahead buffer, and transformer-based contextual layers. To further reduce inference time, the model generates waveforms directly via a neural vocoder, thus removing intermediate mel-spectrogram conversions. Finally, DarkStream anonymizes speaker identity by injecting a GAN-generated pseudo-speaker embedding into linguistic features from the content encoder. Evaluations show our model achieves strong anonymization, yielding close to 50% speaker verification EER (near-chance performance) on the lazy-informed attack scenario, while maintaining acceptable linguistic intelligibility (WER within 9%). By balancing low-latency, robust privacy, and minimal intelligibility degradation, DarkStream provides a practical solution for privacy-preserving real-time speech communication.