Yes, that’s correct.
The cloze note type is treated specially by Anki, and cannot be created based on a regular note type. If you wish to customize it, please make sure to clone the existing Cloze type instead of another type of note. Things like formatting can be customized, but it is not possible to add extra card templates to the cloze note type.
– Adding/Editing - Anki Manual
No, it says to change the note type –
What would you rename it to? And why? 
It’s not a situation where you have multiple cards that display different things and you need to differentiate. It’s just one card template.
Every card you create from a cloze note is going to be named “Cloze #” based on the # of the cloze marker that creates it – so you wouldn’t be able to rename them one-by-one anyway.