In recent years, Deep Neural Networks (DNNs) have achieved impressive results in image recognition, but they are difficult to be deployed on edge devices due to their growing complexity. Split Computing (SC) addresses this issue by partitioning DNN processing on edge and cloud. Dynamic Split Computing (DSC) extends SC by selecting the split point based on runtime conditions such as network bandwidth. For DSC, privacy concerns still exist – for example, model inversion attacks could reconstruct original inputs from intermediate outputs sent from edge to server. This work studies a first attempt of applying differential privacy to DSC. We propose a privacy-aware DSC training method as well as a DSC selection algorithm for both privacy and latency improvement. Experiments show that our training improves accuracy by up to 51.1% and mitigates privacy risks against inversion attacks.