There are various compounds in nature which are white.
One of these is Titanium Dioxide
Titanium dioxide, also known as titanium(IV) oxide or titania, is the naturally occurring oxide of titanium, chemical formula TiO2. When used as a pigment, it is called titanium white.
Another of these is Lead Carbonate, or white lead
White lead is the basic lead carbonate, 2PbCO3·Pb(OH)2. It is a complex salt, containing both carbonate and hydroxide ions. White lead occurs naturally as a mineral, in which context it is known as hydrocerussite, a hydrate of cerussite. It was formerly used as an ingredient for lead paint and a cosmetic called Venetian Ceruse, because of its opacity and the satiny smooth mixture it made with dryable oils. However, it tended to cause lead poisoning, and its use has been banned in most countries.
Now, to have a white looking moon, you don't need the entire body to be made of this material, but just to have the surface layer being covered with it. Which helps if your material is not that abundant.
Parking aside the issue of abundance, you need to cope with depositing of other dust, which will be most likely not be as white as the background.
So, it is possible though not highly likely. And even then, without a mechanism constantly refreshing the white surface, it won't last long.