As advancements in technologies like Internet of Things (IoT), Automatic Speech Recognition (ASR), Speaker Verification (SV), and Text-to-Speech (TTS) lead to increased usage of intelligent voice assistants, the demand for privacy and personalization has escalated. In this paper, we introduce a multi-task learning framework for personalized, customizable open-vocabulary Keyword Spotting (PCOV-KWS). This framework employs a lightweight network to simultaneously perform Keyword Spotting (KWS) and SV to address personalized KWS requirements. We have integrated a training criterion distinct from softmax-based loss, transforming multi-class classification into multiple binary classifications, which eliminates inter-category competition, while an optimization strategy for multi-task loss weighting is employed during training. We evaluated our PCOV-KWS system in multiple datasets, demonstrating that it outperforms the baselines in evaluation results, while also requiring fewer parameters and lower computational resources.