The department I will be getting my degree from and my research area have very little in common
No! It is NOT a big deal. This case is not so important because nowadays the research is interdisciplinary more than any time. Faculty members affiliated with a specific engineering department are even highly-involved in a vast variety of projects with their peers in other departments. The most important thing is being productive as a Ph.D. student within your studies. It requires interest in your research + coherent interaction with your supervisor.

You may have two plans for the future:


If you would like to involved in industrial positions: They actually do not care much about your major and degree's field, but your professional credentials and your practical capabilities. As an instance, assume that you're interested in working as a robotic engineer. As long as you show potential signals to be a right candidate for the position, MechE degree, SysE degree or something else would not hurdle your way.
If you're eager to work in academia: Just do your best to flourish your publication trace. As long as you both have a fruitful Ph.D. and show enthusiasm for research, most of vacancies related to your research in various departments (such as ECE, MechE, CS, etc.) will be open to you, POTENTIALLY (don't underestimate current competition for restricted tenure-track positions!)


Best