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The official chemical naming system was established by a group called the International Union for Pure and Applied Chemistry (IUPAC). Organic compounds containing carbon are usually the most difficult to name and must follow a very strict set of rules but inorganic compounds not containing carbon also have nomenclature rules. Oxygen gas has the formula O2, meaning it is composed of two oxygen atoms bonded together via a double bond. Understandably, this is a chemical compound that has been known about for centuries and as such has many common names associated with it for historical sake. It is most commonly called simply "oxygen," but obviously this can lead to confusion with referring to the general element oxygen as well. Therefore, it is more appropriately named either "dioxygen" to denote O2 versus O or "molecular oxygen," again to denote a complete molecule O2 versus the general element O. So the best name for oxygen gas is either dioxygen or molecular oxygen. In terms of systematic naming, dioxygen is probably best.
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