Human cognition of new concepts is inherently a streaming process: we continuously recognize new objects or identities and update our memories over time. However, current multimodal personalization methods are largely limited to static images or offline videos. This disconnects continuous visual input from instant real-world feedback, limiting their ability to provide the real-time, interactive personalized responses essential for future AI assistants. To bridge this gap, we first propose and formally define the novel task of Personalized Streaming Video Understanding (PSVU). To facilitate research in this new direction, we introduce PEARL-Bench, the first comprehensive benchmark designed specifically to evaluate this challenging setting. It evaluates a model's ability to respond to personalized concepts at exact timestamps under two modes: (1) Frame-level, focusing on a specific person or object in discrete frames, and (2) a novel Video-level, focusing on personalized actions unfolding across continuous frames. PEARL-Bench comprises 132 unique videos and 2,173 fine-grained annotations with precise timestamps. Concept diversity and annotation quality are strictly ensured through a combined pipeline of automated generation and human verification. To tackle this challenging new setting, we further propose PEARL, a plug-and-play, training-free strategy that serves as a strong baseline. Extensive evaluations across 8 offline and online models demonstrate that PEARL achieves state-of-the-art performance. Notably, it brings consistent PSVU improvements when applied to 3 distinct architectures, proving to be a highly effective and robust strategy. We hope this work advances vision-language model (VLM) personalization and inspires further research into streaming personalized AI assistants. Code is available at https://github.com/Yuanhong-Zheng/PEARL.