To the user, this looks like a disfunctional thing (usually greying out
is used for props having no effect).

The greying out is caused by rB8b7cd1ed2a17: Painting: Canvas switcher for painting brushes/tools..

Above commit disabled the direct renaming of images in the
TEXTURE_UL_texpaintslots UIList (and instead displays the texture slot
directly as a prop -- which has its PROP_EDITABLE flag cleared)
(from the commit message):

A limitation of this patch is that is isn't possible anymore to rename
images directly from the selection panel. This is currently allowed in master.
But as CustomDataLayers aren't ID fields and not owned by the material
supporting this wouldn't be easy.

To work around the UI confusion (but still keep the non-editable nature
of the property), now just display this as a label.