A new mineral is approved and named at the Commission on New Minerals and Mineral Names (CNMMN) of International Mineralogical Association (IMA). So any mineral name is named by using alphabet after the place where the mineral was recovered, a person who contributed to mineralogy or discovered it, or shape and color of the mineral.
However mineral species tend to be divided by the trivial difference and number of mineral species increases more and more. For example, plagioclase group had been classified by the ratio of Na and Ca to albite- oligoclase-andesine- labradorite-bytownite- anorthite. This classification was reconsidered and re-classfied to two end members of solid solution: albite and anorthite. It is beneficial for everyone to name minerals systematically like this.
In 2007, it is decided that prefix showing chemical composition of minerals must be changed to suffix nomenclature at CNMMN of IMA. For example, chlor-, fluoro-, hydroxyl-, and strontium- were used for some group minerals such as apatite and apophyllite. These names were changed to apatite-(CaCl), apatite-(CaF), apatite-(CaOH), and apatite-(SrOH). This suffix nomenclature was applied to minerals containing rare earth elements (1960's), zeolite (1997), and epidote (2006). This expression is very useful because we can directly recognize chemical composition and same mineral group will be at a block when mineral names were alphabetically sorted. I personally want to encorage these activities. You may think of names such as garnet-(FeAl) and garnet-(CaFe), but most of IMA members make much of person's name and local name. At the same time, deleting diacritical marks such as accent and umlaut from mineral name was proposed but it was rejected to remain person's name and local name correctly. Exception is the cases where diacritical marks were used without no relation to person's name or local name. However, apatite group name was changed agein to old chlor-, fluoro-, hydroxyl- preffix system in 2011.
At Smithsonian Museum (Washington DC, USA), I found very interesting trial. Solid solution minerals and variety name of a mineral with different color such as jewels were described clearly as a variety species. For example, oligoclase is described as albite var. oligoclase. The definition of species of animals and plants is breeding, and solid solution is thought to be "breeding" in the world of mineral. So I agree with this classification way. As the mineral phase is defined by frame work structure, "mineral species" may be united based on their frame work structures.
This description way is very useful because it can include jewel name which has been only a useful field name. Ruby and sapphire have been used in applied physics as an academic term, but they are ignored in mineralogy. Here we can use them as corundum var. ruby or corundum var. sapphire. Anyway I can not imagine anything by the name of Osarizawaite, but Alunite var. Osarizawaite is better to understand what it means.