How does closing down a department affect a PhD student?
I will try to address some specific questions/concerns you pose. My comments are based on observations I made (and continue to make) as an MA and PhD student, and administrative staff member at a research center. I haven't seen this exact situation happen, but I've seen and contributed to many other restructuring events (advisor moving to another university, founding new department/lab/research center...).

In academia, the most important indicator of the value of your PhD is the quality and quantity of the research you do. While factors like your advisor, the team at your lab, the facilities available, etc. can affect this indicator, the name of the department you graduate from probably will not. In fact, it is not uncommon for researchers who have studied one field to be employed in a differently-named field. One example is Don Norman, who studied engineering and then psychology, and works in the field of design. The decision to close or merge departments most likely will have no bearing on the value of a PhD.

It is common for people doing work in a specific field (e.g. transportation) to have credentials or employment in a more general field (e.g. management, computational science), or vice versa. More generally, subject matter of your work and the discipline or methods you use to approach that subject can be different. It is normal for one's credentials or employment to relate to only one of these things. It is perfectly acceptable to be a researcher who deals with transportation (subject matter) using computational science (approach), while having credentials in management (general field).

In sum, the "person of interest" actually appears to have the right idea. While your concerns are valid, one's relationship with their advisor and lab/team is often a much more important factor, compared to the name of the deparment they belong to and the courses that are available.