Photos and EXIF data

On the iPhone you are setting the caption of a photo, not the title.

When you sync the photos from the iPhone to the Mac with iCloud Photos, the captions you are adding on the iPhone will appear as captions in Photos for Mac, not as titles.

I do ot have a windows PC, so K. cannot gets how to transfer these tags to a windows PC.

No, the info is not stored in the exif. Photos is always leaving the unmodified originals unchanged. The faces are stored in database files in the Photos Library and are synced with iCloud Photos to the Photos Libraries on other Apple Devices.

There are third-party apps that allow to view and modify the exif tags of photos. I am only using them to inspect exif tags. The versions that allow to modify the tags are not free.

When I add text to the caption of a photo on my iPhone, then share it by mail at the full size as a mail attachment, the saved attachment will be showing the caption in the exif tags. With exiftool I am seeing them in the tags "Image Description", "Description", and "Caption-Abstract".

So you could try to write the recognised faces to the caption and Mail the photo.

I also tested to download the photo from an iCloud link, but then the caption has been missing.