Can we rename the field CloseDate of the stage history related list of opportunity?
Beside, is there a way to increment the value of this field?
You can change this via Build / Customize / Tab Names and Labels / Rename Tabs and Labels.
As to the second question: what exactly do you mean with 'increment'? You can change this field into whatever value you want. Except when it's in the history list, because you can't change the past.