Imported photos to ip[hone but lost the folder names

Have you been syncing the photos with iTunes to the iPhone?

if you just want to be able to view the photos on the ipHone and do not need them in the full resolution, you could sync them to the iPhone with shared albums. Shared Albums do not need paid cloud storage. Share a new shared album for each album of photos you want to transfer from your Mac to the iPhone. See: Use Shared Albums in Photos - Apple Support

But iCloud Photos Library, as recommended by OPT, would be the best solution, because it will simply keep the Photos Libraries on your iPhone and your Mac identical, and is perfect for syncing the Portrait Mode photos and Live Photos between the devices, and all adjustments you apply.

To maintain folder/album continuity one must enable the iCloud Photo Library on both devices. If will probably require purchasing additional iCloud storage to house your library on line.

The image files would be in your Photos Library and in the online iCloud Photos library. Any change made to a photo in your local library will be replicated in the online library.

If you are strapped for space on your Mac you can select the option to have optimized versions of the image files stored on your Mac with the full sized version online. However, any time you want to use the full sized version, i.e. slideshows, making books, printing copies, etc. you must wait for the full sized version to be downloaded to your local library.

Any photo taken on the iPhone will be added to the iCloud Library and your Mac's Photos library. It will also be on your iPhone unless you opt for the Optimized storage.

The idea is to keep all devices, i.e. iPhones, Macs, iPads, etc. that are signed into the same Apple ID and have the iCloud Photos library enables have the exact same library.

None of Apple's photos apps speak "folder"

They use tags and metadata to sort content. All photos reside in one "album"