Does water have a chemical name?
TL;DR IUPAC hasn’t made up their mind, but plain old water appears to be an appropriate name. However, chemical derivatives of water may not be named using water.



In Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names 2013 it is stated (P-21.1.1.2) that


  The common names water, ammonia, [...] are used in these recommendations but their use as preferred IUPAC names is deferred pending publication of recommendations for the selection of preferred inorganic names; thus, no PIN label will be assigned in names including them.


I’m not sure when the next edition of the Red Book (i.e. inorganic chemistry nomenclature recommendations) is coming out, but I can quote the relevant section from the most recent version.

Table IR-6.1 of Nomenclature of Inorganic Chemistry: IUPAC Recommendations 2005 lists "oxidane" as the parent hydride name for $\ce{H2O}$. However, it also adds the caveat that


  The names ‘azane’ and ‘oxidane’ are only intended for use in naming derivatives of ammonia and water, respectively, by substitutive nomenclature, and they form the basis for naming polynuclear entities (e.g. triazane, dioxidane). Examples of such use may be found in Section IR-6.4 and Table IX.


Therefore the compound $\ce{ONONO} = \ce{(ON)2O}$, a nitrosylated derivative of water, is named "dinitrosooxidane" and not "dinitrosowater". More examples may be found in Table IX of the same publication.

Water itself is still called water. For example, tritiated water $\ce{H^3HO}$ is named (3H1)water (Section IR-2.2.3.2).