I created a new custom object.
I wanted to fix typo error of my API name before publish.
But Edit Object dialog does not have a field 'API name'.
Create Object dialog
Solved! Go to Solution.
I agree with Greg. It's not currently possible to change the api name once you've created the object, so you would need to create a new one with the correct api name. You should definitely submit an idea on this though, as that will allow others to add their voice as well.