Process mining (PM) techniques extract insights from event logs to discover, monitor, and improve business processes. The quality of input data significantly impacts the reliability and accuracy of these insights. Existing approaches to detect and repair these issues are limited to offline data pre-processing. Given the potential of real-time process analysis to provide valuable business-related insights, online PM has gained interest. However, process-data quality (PDQ) issues in process event streams (PES) beyond anomalous events or traces have not yet been addressed. Existing PDQ management approaches lack the adaptability and incremental processing capabilities necessary for streaming event data and evolving processes. This paper presents a novel approach for dynamically detecting and repairing synonymous, polluted, and distorted activity labels in PES, which are common issues affecting the quality of PM outcomes. By incrementally maintaining stabilised activity control-flow context using memory-efficient approximate data structures, the approach detects and merges similar labels or splits dissimilar labels on the fly. An incremental hierarchical clustering algorithm, incorporating decaying and forgetting mechanisms, is employed for the dynamic repair of similar activities, ensuring efficiency and adaptability. The approach is validated using publicly available real-life logs from two hospitals.