What is the official name of the smallest and simplest cells?

The official scientific name for the smallest and simplest cells is prokaryotes. Prokaryotes are single-celled, the smallest and most primitive organisms that can live independently. Prokaryotes are one of the two broad cell classifications, the other one being eukaryotes

The cell structure of a prokaryote consists of a cell wall, cytoplasm, cell membrane, flagella, ribosome, pili, plasmids and the nucleoid region. Prokaryotes have no true nucleus; the DNA is not separated by a membrane, but is in the nucleoid region. Prokaryotes are divided into bacteria and archaea, and they can exist as single-celled organisms or form multi-celled structures. They can live in extreme habitats, such as hydrothermal vents, hot springs, swamps, wetlands and the guts of animals.