Is the name "Dihydrogen monoxide" actually what chemists would use to refer to $\ce{H2O}$ (assuming there was no common name, "water")?
Of course, this is all over the internet. I'm a little skeptical though because the similar chemical $\ce{H2S}$ is called "hydrogen sulfide", not "dihydrogen monosulfide".
No, it's not. The "dihydrogen monoxide" name is used as part of a hoax. In the scientific community, there are chemical names for water, and which one is used in the literature generally depends on how it interacts with something else (hydroxic acid and hydrogen hydroxide were two I heard most often in acid-base reactions).
IUPAC, the standards committee that sets standard names for chemical structures, suggests "oxidane" as a starting point for the construction of other names for chemicals that are derived from water. However, they do not suggest "oxidane" itself be used to refer to plain water.
Most chemists would use "water", even when writing scientific papers.
Like most of the other professionals answering here, I've given a couple of talks on international conferences and published some articles in peer-reviewed journals.
I have never used the terms dihydrogen monoxide or oxidane and do not intend to do so in a serious, scientific context.
Typically, one talks and writes about water, aqueous solutions and even uses a (traditional) term like brine when referring to an aqueous, saturated solution of sodium chloride.
I agree with the other answers. No serious chemist uses any word other than "water" in whatever language the chemist uses.
However, the name does appear to be following the established rules for the systematic naming of binary main group covalent compounds.
Take for example $\ce{N2O5}$:
We need this sort of system to give us unambiguous names for binary compounds, especially when, for example, there are multiple oxides of nitrogen: $\ce{N2O}$, $\ce{NO}$, $\ce{N2O3}$, $\ce{NO2}$, $\ce{N2O4}$, and $\ce{N2O5}$.
Note that we rarely use the "mono-" prefix: $\ce{NO2}$ is nitrogen dioxide.
And we never use prefixes with the binary hydrides. The acidic ones are all named like ionic compounds, as are the metal hydrides, and the non-acidic ones all have common names that are used so frequently it is silly to use more complex names:
Water would thus be hydrogen oxide if anything.
Even though there are other possible oxides of hydrogen (or hydrides of oxygen), they have different names based on the anions:
