Looking at your map in Tears of the Kingdom, you might notice that each lightroot is directly beneath a shrine. However, something I noticed when watching a video on Youtube is that the Nisoij lightroot is directly beneath the Jiosin shrine. While this isn't obvious, these names are the same, but spelled backwards. Does this relationship hold true for every shrine and lightroot pair?
Based on the Lightroot wiki, your analysis is correct.
The name of a Lightroot is the name of the above shrine, but backwards.
Yes, every lightroot's name is the name of the corresponding surface shrine reversed.
Interestingly, however, the assertion that every lightroot is directly beneath a shrine is does not hold. I've encountered three lightroots (I don't recall which, though I could check again) that are not directly beneath their corresponding shrine, but rather about 10-100 meters offset.