What cause the names of the photo albums to change randomly a week or two after sync?

Hi. Your problem is caused by mixing the incompatible concepts of Folders and Albums. iOS Photos stores all photos together in the Camera Roll. You can think of it as a folder, but it's really just a collection. The albums are virtual selections from the collection. You can think of them as lists selecting items from the Camera Roll. Each photo can be in one or more albums, or in no albums. As you can see, this is quite different to the concept of folders holding individual files. There have been other posts on this over the years, but I don't think there is any complete solution, save using an iPhoto app on an Apple computer.

Straight after each update for the past 2 or 3 years my synced photos have got messed up. Albums that I used to have on my iPad (but which I removed a number of years ago) have re-appeared, with my currently synced photos spread throughout those albums (each album has the number of photos that used to be in them, they just contain a seemingly random selection of my current synced photos) - I still have the correct synced albums as well as the wrong ones.

The way I fix it is to reconnect to my computer, de-select one of my albums (the one with the fewest photos), sync, and then re-select that album and re-sync

I have no idea what Diana talked about. It doesn't even sound like it's related to your question. Sorry, Diana. I can however relate to King Penguin's experience.

For the past few years, when I update iOS, my synchronized photo albums get scrambled after every iOS update. It is exactly the same as your experience but mine is triggered by iOS update. If I don't update iOS, my sync'd albums remain the same.

Your problem seems more severe if your sync'd albums get scrambled for no reason. Try factory restoring the device.