You can just re-import the pictures into a new Lightroom catalogue. On Importing the files, you can specify a folder structure and even a filename-pattern, that Lightroom applies while it's importing.

To successfully do that, you need to do the following steps:

1. Make sure that all lighroom adjustments are saved to either xmp-sidecar files or into the files themselves (e. g. DNG-Files can do that), you can do so by either enabling that option in the catalogue-settings, or selecting ALL images and using the function Metadata > Save Metadata to file (Strg+S or CMD+S)
2. If you have any virtual copies, export them first as DNG, or they will be lost in the process
3. Now create a new catalogue in lightroom, go to import and navigate to the folder where your images are in
4. In the import select copy to keep a backup of the old catalogue around in case something goes wrong
5. On the right side you can now specify the Folder Structure Lightroom should create (also multiple "By Date" Variations), select one that you like
6. Now click on import. Lightroom should recognize all keywords and development settings.
7. After the import, if you have any smart-collections you want to keep, you can go to File > Import from other catalogue and select your old. Now select only a single photo to import, and do nothing about its location. You can delete it from the "Last import"-Collection later. This import wir copy all collections from the old to the new catalogue, but the non-smart collections will be empty.
8. Don't forget to import the previously exported virtual copies. If you like you can create new virtual copies in your new catalogue and transfer all development settings from the dng files, or you can just keep the dng around.