I can hardly think of any use cases for this except a static collection/watched list or to pickup an inactive list to be honest.
In my opinion this could/should be something you can launch from your list page or the options only.
I don't want to sound salty but there are already duplicates, adding more because someone needed it on his profile isn't helping.

Why do you find it worrysome?

I find the feature as easily accessable it is already worrysome so forcing people to pick a name to prevent clutter seems to be little trouble imho. This will also prevent missclicks and provide a clearer transition to the copy.

The main reason I didn't do that was I figured you can edit and delete the list once it refreshes to the next screen if you need to. Didn't want too many prompts before actually cloning it.

I think there are valid use cases for wanting to clone one of your own lists which is why I didn't limit it.

Also hide the option from yourself (imho)