I am involved in a peculiar PhD situation. I am working full time at a government lab that is fairly new (<10 years of existence), but has however attracted some strong names in my field (Computer Science and Data Management) as appointed researchers. Government labs do not issue PhDs, so I had to enroll at a university. The university that I enrolled at (not my choice) is among the top 10 in my country, but lies in the top ~1000 area worldwide. Furthermore, my advisor is not really involved in my work and is generally active in somewhat different research directions. However, I had very good funding so I decided to treat this as exactly what it is, i.e., a formality, as I can't get my PhD from the government lab.
During the past four years, I have been very productive and managed to create a solid publication record at A-level and A*-level conferences and journals, as well as a decent citation count (~150). I am first author in most of my papers, and some of the people I worked and published with are very established and acclaimed academics in this field.
Before starting my PhD, a obtained an Electrical Engineering degree and a Masters degree from top schools in worldwide rankings. Now my question is, do I need to somehow reflect this situation in the form of a justification of why I am getting my PhD from an unknown university? Or the fact that after two excellent school names, I have this third name in my CV that is unknown and overall a weird addition?