The proliferation of Data as a Service (DaaS) available on the Internet and offered by cloud service providers indicates an increasing trend in providing data under Web services in e-science and business domains. While data usage and selection are dependent on different constraints established on the basis of several data concerns, for example, quality of data and data privacy, existing data service engineering approaches lack techniques to allow the evaluation, association and publishing of such concerns with data provided via DaaS. Furthermore, data sources behind DaaSs are not static but dynamically changing, thus requiring the evaluation and publishing of data concerns to be dynamic and on-the-fly as well. In this paper, we present a novel data concern-aware service engineering process for evaluating and publishing data concerns inside DaaS that covers different evaluation and publishing scopes, modes, and integration models. Based on our process, we present a framework and its implementation for the evaluation and publishing of quality of data metrics associated with data provided by DaaSs. In this paper, we also perform several experiments to demonstrate our framework.