Q: Organizing photos on Photos for Mac

To reduce the clutter, you can add folders (File Menu > New Folder) & drag any user created albums (in your screen shot, everything in iPhoto Events) into them. You can also put folders in other folders, similar to how your Animals folder is in your iPhoto Events one. With the Sidebar visible, this is easily done by drag & drop.

Edit: you can also rename albums & folders by right-clicking on their names & selecting that option from the popup menu.

Everything in the iPhoto Events folder is a converted iPhoto Event. If that is what you mean by 'left from iPhoto,' you can delete the album (but not the photos in them) if you want. If you mean anything in the iPhoto Library, see Photos saves disk space by sharing images with your iPhoto or Aperture libraries - Apple Support or (Six Colors: The (hard) link between Photos and iPhoto for a more technical explanation) of how the two libraries share photos.

To get the buttons at the top, hide the Sidebar (from the Views menu).