Efficient issue assignment in software development relates to faster resolution time, resources optimization, and reduced development effort. To this end, numerous systems have been developed to automate issue assignment, including AI and machine learning approaches. Most of them, however, often solely focus on a posteriori analyses of textual features (e.g. issue titles, descriptions), disregarding the temporal characteristics of software development. Thus, they fail to adapt as projects and teams evolve, such cases of team evolution, or project phase shifts (e.g. from development to maintenance). To incorporate such cases in the issue assignment process, we propose an Online Machine Learning methodology that adapts to the evolving characteristics of software projects. Our system processes issues as a data stream, dynamically learning from new data and adjusting in real time to changes in team composition and project requirements. We incorporate metadata such as issue descriptions, components and labels and leverage adaptive drift detection mechanisms to identify when model re-evaluation is necessary. Upon assessing our methodology on a set of software projects, we conclude that it can be effective on issue assignment, while meeting the evolving needs of software teams.