in the same order of idea
Your system allows to give a same name at different objets (not in the same time with a separated selection) why not :)
But does it possible to have an alert message who say something like "Name is yet existing!" when you create a new object?

idem for a nature of object (cube, sphere,...) a cone named "bil" is yet existing
idem for colors....a blue object named "bil" is yet existing
idem for the blender : a blue box named "bil" is yet existing!

Because if you have (without remember that for any reason) some objects with the same name (nature, color) you can erase some others than the first one wished!
So another alert message "Carreful you erase some objects with the same(nature, colors) name!" so "are you sure: Yes / no?" ;)

Of course you have the up right side "window infos" with written "3 solids" but we never think to read it ;)