I don't think that number of photos is part of the problem, I've got around 3500 stored on my microSD card, a relatively modest number as I know a number of people who regularly keep 10,000 or more in their photo libraries.
As for renaming established folders on your microSD card using your computer, it sounds like your computer may have read permissions to those folders but not necessarily write permissions. Another thing to keep in mind is if you are going to change the names of some folders, because the Android operating system and some apps may have settings that point directly to those specific folders as their defaults, by renaming them may cause bring about odd behavior issues -- i.e. the default folder for photos is the 'DCIM' folder (Digital Camera IMages). If you don't want to use that folder to store your camera photos, you need to go into the settings menu of your camera app and re-direct it to the folder you do want. You also should check the settings menu of your photo managing app (Gallery, Google Photos, etc.) so once you stop using that default DCIM folder it's going to also scan and index the folder you've set as your new default, photo storage. You might also need to check the settings menu of your texting app so instead of looking in the DCIM folder for photo attachments, it's looking at your new photo storage folder.
I'd leave something like the photo default storage folder as is, there's a lot of operational things in our phones that are preset to rely on it. Depending on which photo managing app you're using, it won't display your photos sorted by whatever folders and sub-folders you create anyway, it's going to present everything it detects as a flat, all in one window display. Better to use the app's 'Albums' feature to sort and organize your photos -- the photo files themselves are still just stored in that DCIM folder, but using different albums you can display them in the different groupings that you prefer.
What photo manager app are you using? Gallery? And which file manager app on your phone did you initially try to rename/add those folders?