Q: Faces in Photos do not sync across different computers

It is very frustrating that Faces in the Photos app (Yosemite and El Capitan) do not sync across different devices. Is there any possibility of this functionality being given to Photos in the future?

Perhaps, if enough users send feedback to request this feature.  Here is a feedback form.

The next version of Photos will probably not yet include this feature. It is not listed with the improvements that are announced by Apple for the Photos update to come with El Capitan:   Apple — OS X El Capitan

It only promises a streamlined workflow for faces, whatever that will be.

Everything in its place.

Photos has been fine-tuned to make it even easier to manage your library. Now you can add a location to a single image or to an entire Moment. Naming your favorite people in Faces is faster with a streamlined workflow. You can also sort your albums — and the contents inside them — by date, title, and more.

It is highly tedious having to carry out the same faces recognition on two different machines accessing the same set of photos.

That's true. And I have to do that even on four different Macs.

But at leasts searchable  face names sync with the photos, only not the faces thumbnails.

If you assign a name on one mac, you can search on the others for that name and identify the photos that need naming.

Use Photos and iCloud Photo Library on multiple Mac computers - Apple Support

After you sign in, these items appear in the Photos app on all of your Macs:

• All original photos and videos
• All folders and albums
• Smart Albums
• Keywords
• Searchable keywords based on Faces tiles
• Key photo selections

These items are available only on the Mac where you created them:

• Books, cards, and calendars
• Slideshows
• Keyword shortcuts
• Unused keywords
• Last imported album (this album contains photos you most recently imported on a specific Mac)
• Faces tiles and Faces data