Should I change my Ph.D. department to better reflect the nature of my project?
While we cannot tell you the regulations of your institution on changing departments, I would like to suggest that it's likely to be not worth the bother.

Every department covers a complex network of subjects, and so having a degree that says "Physics" will not really be any more informative than one that says "Civil Engineering." It's also not at all unusual for a Ph.D. to be something that might be reasonably categorized under multiple departments---in fact, it is quite common for research to be interdisciplinary, and especially for the "home field" of a method to be different than the "home field" of an application area. Finally, departments and degree names are not particularly consistent in their names and interpretations from institution to institution.

As such, people will in general pay attention to the content of your research much more than the particulars of your department.

If you actually find some major impediment to continuing in your current department, that is a different matter, but it doesn't sound like that is currently the case---particularly so early in your time as a graduate student.

In short: don't worry about categorization, worry about executing your project.