There isn't a single, universally accepted "official name" for the smallest and simplest cells. However, depending on what we are focusing on, we can use different terms:

* Mycoplasma: These are the smallest known bacteria, often referred to as having the "smallest genome" and being very simple in terms of their structure. They are often used as model organisms to study fundamental biological processes.

* Prokaryotes: This group broadly encompasses bacteria and archaea, which are characterized by lacking a nucleus and other membrane-bound organelles. While they can be quite complex, they are generally considered simpler than eukaryotic cells.

* Bacteria: This specific group within prokaryotes is often associated with simplicity due to their lack of a nucleus and other complex features.

Ultimately, the best term to use depends on the context and what aspect of the cell you are emphasizing.