I've been speaking with a professor with regards to admission into a PhD program at a top European University, and things have been going well so far. The only problem is that it isn't "officially" in my field of choice.
To be more specific, the degree label will be "Mechanical Engineering" (as it was for my B.Eng and M.Eng), while most of the work will involve Numerical Computing and 3D graphics; just that it will be in the Mechanical Engineering domain. In fact, one of the reasons the professor has expressed interest in hiring me is because it isn't common for Mechanical Engineers to also be experienced programmers in the field.
While I'm certainly excited at the opportunity, I am also feeling a little bit reluctant, because I wanted my degree to be titled "Computational Science" or "Software Engineering". The reason being is that I don't want to be seen as an "inexperienced" developer after spending 4 years in a program doing exactly that. The concern might seem shallow, but I don't want to commit 4 years of time I could be using to further my career.
Regardless of my reasoning, is it possible/common to ask for admission into a different faculty than my supervisor, while still being supervised by them? How much effort, if any, should I expend to make sure that the field I am accepted in is the one I want, while working with the same professor? What alternatives are there to advertise my qualifications as a software developer/computational scientist if I choose Mechanical Engineering? And finally, if at all, how will this limit/extend my options in the future?
There is no general answer. You should check the university's regulations. Additionally, you should talk with your potential supervisor about the issue. Even if it's not allowed, he might know a way to circumvent it.
Moreover, I think that the title itself is secondary. The most important part is what you did during your PhD. (To illustrate the point: after that PhD-project, nobody will hire you to design a car engine just because you have a PhD in mechanical engineering.)
If employers have a job opening, they are looking for somebody with the skills necessary for the job. Typical job offers usually include the phrase "desired qualifications: a PhD in computer science or something equivalent." This translates to "we think that somebody with the necessary skills will have a degree in computer science but if you possess these skills and a different PhD, we still want you to apply."
The place to present your software development skills is your cover letter and your CV/resume once you apply for positions. Make there very clear why you are the perfect fit for the position. For instance, in the CV, you should list the software you developed and the languages you programmed in (with number of years you are using them); and in the cover letter, you explain how these things qualify you for the position.