With the rapid growth of Artificial Intelligence, Large Language Models (LLMs) have become essential for Question Answering (QA) systems, improving efficiency and reducing human workload in customer service. The emergence of Vietnamese LLMs (ViLLMs) highlights lightweight open-source models as a practical choice for their accuracy, efficiency, and privacy benefits. However, domain-specific evaluations remain limited, and the absence of benchmark datasets reflecting real customer interactions makes it difficult for enterprises to select suitable models for support applications. To address this gap, we introduce the Customer Support Conversations Dataset (CSConDa), a curated benchmark of over 9,000 QA pairs drawn from real interactions with human advisors at a large Vietnamese software company. Covering diverse topics such as pricing, product availability, and technical troubleshooting, CSConDa provides a representative basis for evaluating ViLLMs in practical scenarios. We further present a comprehensive evaluation framework, benchmarking 11 lightweight open-source ViLLMs on CSConDa with both automatic metrics and syntactic analysis to reveal model strengths, weaknesses, and linguistic patterns. This study offers insights into model behavior, explains performance differences, and identifies key areas for improvement, supporting the development of next-generation ViLLMs. By establishing a robust benchmark and systematic evaluation, our work enables informed model selection for customer service QA and advances research on Vietnamese LLMs. The dataset is publicly available at https://huggingface.co/datasets/ura-hcmut/Vietnamese-Customer-Support-QA.