Short answer: There is for now no possibility of getting the option "Organize Desktop by Name" back, apart from developping the source code of the Gnome Shell extension that provides desktop icons in Ubuntu 19.10.
Since Ubuntu 19.04, icons on the desktop are being implemented through a new Gnome Shell extension Desktop Icons. As this is a quite recent extension, it probably is not quite finished, and several functions that were available in nautilus have not yet been implemented in the extension.
Workaround: One could remove the Gnome Desktop shell extension, and then replace the file manager 'nautilus' by 'nemo', which still provides the functionality, but then it might be easier to switch to the cinnamon desktop altogether, or move to xfce or another desktop where desktop icons continue to be fully supported.
Short answer: There is for now no possibility of getting the option "Organize Desktop by Name" back, apart from developping the source code of the Gnome Shell extension that provides desktop icons in Ubuntu 19.10.
Background: In Ubuntu 18.04, it was still the file manager 'nautilus' that provided the icons on the desktop. Gnome developers removed that function in newer versions of nautilus. In fact, Ubuntu 18.04 still shipped with an older version of nautilus to be able to keep the desktop icons.
Since Ubuntu 19.04, icons on the desktop are being implemented through a new Gnome Shell extension Desktop Icons. As this is a quite recent extension, it probably is not quite finished, and several functions that were available in nautilus have not yet been implemented in the extension.
Workaround: One could remove the Gnome Desktop shell extension, and then replace the file manager 'nautilus' by 'nemo', which still provides the functionality, but then it might be easier to switch to the cinnamon desktop altogether, or move to xfce or another desktop where desktop icons continue to be fully supported.