This notation has come up in a paper I'm co-working on. We're currently calling $$\{\{1\},\{2\},\ldots,\{n\}\}$$ the partition of singletons. This name seems suitable. However, I'm not sure what to call $$\{\{1,2,\ldots,n\}\},$$ and I'm guessing there's a name for it in the literature that I'm unaware of.
Question: What is an appropriate name for the partition $\{\{1,2,\ldots,n\}\}$ of the set $\{1,2,\ldots,n\}$?
I don't know an official name, but I would call it a monoset.