> According to the following article, a fsync is also needed on the 
> directory after a rename. I don't understand if is it always needed for 
> an atomic rename, or if we only need it for the "atomic write" pattern.

It's not needed if you just want atomicity, i.e. the file is visible either under its old name or its new name, but not neither or both.
If is however needed if you want durability, i.e. you want to guarantee that the file is visible under its new name after your atomic_rename returns.