You can rename anything you enchant as part of the enchanting process.
I do it all the time to group my worn items.
IE a vampire character tends to have vampire rings, vampire amulets,
vampire cloak, vampire clothes etc just so it's all together in the list
and doesn't get sold by accident.
If you mean renaming something the game already created, no you can't do
that, but you can easily duplicate those items yourself naming them
anything you want.
If you don't have the skill yet, just temporarily boost it;
player.modav enchanting xxx to raise it to whatever level is needed for
the numbers you need with the soul gems you have.
player.modav enchanting -xxx to put it back to normal.
With a high enough enchanting skill you can create anything you have the
knowledge to make (and since you have the item you can destroy it to
learn how to make it then duplicate it.)
And with absurdly high skill you can create that item even with a petty
I recommend getting the any skill anywhere mod so you can make boots of
water breathing for instance instead of being limited to only rings and
headgear (why they did that I'll never know, but then a lot of the
enchanting system of Skyrim makes very little sense.)