I have come across the name trihydroxy propane for glycerol, which I think should've been Propan-1,2,3-triol.
Why is it named this way? Is there any other rule of nomenclature working?
Glycerol and trihydroxypropane are common names. The IUPAC name is propane-1,2,3-triol. The common name glycerol comes from the root glyco- which means sweet. Glucose, glycogen, and glycerin (another name for glycerol) have the same etymology.
Trihydroxypropane makes sense as a common name because there are only 3 locations for the hydroxyl groups on the 3 carbon chain, so the name is basically unambiguous - multiple hydroxyl groups on the same carbon are not stable (see geminal diols).
Trivial names have stuck around for so long despite their lack of systemization because that's what most people call them including biologists. Think of glyceraldehyde,aniline, pyruvate, toluene etc. There is no choice but to leave these named artifacts as acceptable by IUPAC.