Can I request a Ph.D. in a different department having done research in another?
Talk to your supervisor. This probably differs from country to country (maybe federal state to federal state) and university to university. 

However my experience is that people either want to know if I have a PhD or not, or, if they need more details, then they want to know the topic of my dissertation. The intermediate level of the discipline has never come up. So I would not worry too much about it.