Ask for confirmation before just cloning a list and maybe add the option to set the typical list settings like privacy, title, etc.
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)