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I think what you may find most helpful is to know a bit of the history of element discovery and atomic theory.

The first pure substance containing only the element oxygen to be isolated was dioxygen ($ceO2$), in 1774, though it was called "dephlogisticated air" until 1777 when Lavoisier used the term "oxygen" for the first time. This was some 30 years before John Dalton even proposed the first empirical atomic theory. Back then, we only barely had an understanding of stoichiometry, such that Dalton famously claimed the molecular formula for water was $ceHO$. The fact that dioxygen is a substance made of molecules containing two atoms of oxygen probably wasn't widespread knowledge until at least 1811, with the gas stoichiometry experiments of Amadeo Avogadro.

Basically, for a point in time, we knew that there was a substance composed of a single type of atom, which could not be broken down into anything simpler. This fit the then-prevalent definition of an element; "a pure substance that could not be decomposed into any simpler substance". We knew that Lavoisier's "oxygen" had to be $ceO_n$, for some n, but we had no reason to assume $n neq 1$ for decades. By the time we figured out $n = 2$, the name "oxygen" was already widely used to refer to dioxygen. The fact that $n = 3$ also forms a stable compound in ambient conditions (ozone) would also not be known until 1867. A similar story happened with (di)nitrogen (octa)sulfur, (tetra)phosphorus, and so on. The only elements which form stable monoatomic substances in reasonable conditions are the noble gasses.

There is an interesting aspect to consider behind all this. There are some (such as Eric Scerri) who claim we are doing Chemistry a disservice in muddling together the properties of elements and the pure substances which they make. Nowadays our definition of an element is solely dependent on the number of protons inside an atomic nucleus, with no reference to reactivity or in what form the pure substance can be found. In this sense, the elements do not have "reactivities", "melting points", etc.; these are all properties of the pure substances. The only true properties of the elements are things such as electronic distribution, ionisation energies, and so on. However, it is common to see periodic tables stating the melting and boiling points the pure substances of each chemical element, and even Wikipedia bundles the physical properties of dioxygen with the atomic properties of elemental oxygen. For better or for worse, we're stuck with this subtle ambiguity in nomenclature.

Technically, $ceO2$ is molecular oxygen. $ceO$, atomic oxygen, only exists under rare conditions; e.g. for a very short time after the molecule is dissociated by radiation, or where air pressure is so low that dissociated oxygen does not find a partner to recombine quickly.

Whenever one refers to an element, it is likely in the form of molecules, or metallically bound, except for the (usually) inert gases. The common yellow form of sulfur is as $ceS8$ molecules. However, it is still considered elemental sulfur, not a compound, because all the atoms are of the same type.

BTW, later comments indicate some confusion with the number of protons, found in the nucleus, and the electron cloud, found around it. Think of an atom as a fluffy ball of cotton candy (electron cloud), with a few sugar crystals (neutrons and protons) in the center. When atoms combine to form a molecule, only the cotton candy sticks together; the nuclei are separate, with the same number of protons and neutrons (no croutons, though) as in the atomic element. Nuclei can combine, with enough pressure, and that process is nuclear fusion -- which could be discussed better in the physics section of StackExchange.

In short, an element can be found in molecules; it's still an element.

It's simply a colloquialism for ease of reference. It is sort of like the way we call a heap of corn, corn. Instead of corn off the cob, like the comedian Mitch Hedberg jokes about. He says "corn" should mean "corn on an ear of corn", and a pile of corn kernels should be called "corn off the cob", but since we encounter "corn off the cob" much more often than a big ol ear of corn, we simply call it corn.

The more common something is, the less likely it is to be accurately named, and more likely it be colloquialized.

It would be very odd to try to deny all allotropes of an element that element's name, or to require an additional description as in the phrases "molecular oxygen" or (to exclude non-modal allotropes) "diatomic oxygen". Why would it be odd? Because it may require some very specific descriptions that quickly become distracting, difficult to get right, and unimportant to the point you want to make. This is especially true if an element exists in multiple allotropes, whose chemical reactions of present interest might only care about the overall atom count present.

It's easy to get used to monatomic and diatomic forms of elements (metals usually treated as honorary examples of the former), and forget about such creatures as:

• 
  $ceAs4$ and multiple allotropes that don't admit as neat a formula (which will be a theme),


• 
  $ceB12$ and other allotropes of boron


• 
  $ceO3$, $ceO4$ and $ceO8$
  


• 
  $ceP2$ vs $ceP4$ and multiple polymeric forms of phosphorus


• 
  $ceSe8$ and its crystalline and polymeric counterparts


• 
  $ceS_n$ where $n$ can be any of $2$ to $9$, $15$, $18$ or $20$
  


• and some elements having pretty much no natural $X_mathrmsmall,n$ allotropes such as antimony, carbon, germanium and tellurium.

What would you like to call them all?

"Oxygen" is a set which has "atomic oxygen" and "molecular oxygen" as elements(of a set).
It's like asking why is a "Ford automobile" and a "Chevy automobile", each called an "automobile". So, calling "atomic oxygen", "oxygen" is not inconsistent. Neither is calling "molecular oxygen" oxygen inconsistent.
We can add ozone to this as we can say, "ozone is the triatomic form of oxygen".
There are no inconsistencies here.
Your question is not of science but of grammar. The singular and plural forms of the chemical elements are the same. We don't say, "oxygens", or "aluminums" unless we are talking about a property as "oxygens melting point is...". This question doesn't really belong here, but belongs in the category of English grammar.

Diamond and graphite are both arrangements of carbon atoms, each with very different properties and yet they are both pure carbon, as is a single carbon atom, of course. Likewise $ceO2$ is as much oxygen as atomic oxygen is. The only complication is that what we habitually think of as oxygen is oxygen as a gas comprised of $ceO2$ molecules. Like Humpty Dumpty in Alice in Wonderland, "a word means what [we] choose it to mean" and often we have to add modifiers or alternate terms to avoid ambiguity. Such is language...