Suddenly, thanks to Minecraft, I think I found a possible answer.
Could it be that the creators of Skyrim, and in particular, those who were responsible for the Smithing feature, mistook Obsidian as Ebony, being that the in-game traits of Ebony are incredibly similar to those of Obsidian?
In the wikia page regarding Ebony Ingots, it says that Ebony may be the Skyrim counterpart of Obsidian, but I think it was simply a minor mistake, and referring to the Wikipedia page regarding Obsidian, the physical resemblance between and in-game Ebony Ingot and a real life Obsidian is great.
If this is the case, I'd really like seeing the game's creators switch the names of Ebony and Obsidian, but I'm fine with it either way.
Have a joyful discussion, and sorry if this subject has been already discussed.