"Can you rename a weapon after you've enchanted it and said no to changing the name?"
What an excellent question.
I'm afraid not, friend. Took me some time just to understand how to enchant a weapon in the first place. Hah!
Unfort, barring from some mod or such, your only alt now is to reload from a save file and then make your changes.
As a rule of thumb, before making any permanent changes (such as enchanting or going on some quest) I always save just in case.