Can there be two IUPAC names of a compound?
Generally, since many compounds can have two or more names in accordance with several methods recommended by IUPAC, a compound may be named correctly in more ways than one. Therefore, current IUPAC recommendations include the definition of a preferred IUPAC name (PIN), which is the name preferred among two or more names generated from two or more IUPAC recommendations including the many retained names.

In particular for primary amines, the rules given in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) are as follows.


  P-62.2.1.2 Primary amines, $\ce{R-NH2}$, are systematically named in the following ways:
  
  (1) by adding the suffix ‘amine’ to the name of the parent hydride;
  
  (2) by adding the name of the substituent group $\ce{R-{}}$ to the parent hydride ‘azane’;
  
  (3) by adding the name of the substituent group $\ce{R-{}}$ to the term ‘amine’ used as a preselected parent hydride name for NH3; this method is used only with monoamines.
  
  (…)
  
  Method (1) leads to preferred IUPAC names.


Since, according to the current recommendations, the substituent group $\ce{(CH3)2CH-{}}$ can be named ‘propan-2-yl’, ‘isopropyl’, or ‘1-methylethyl’ (where ‘propan-2-yl’ is the preferred prefix), the compound given in the question can have the following seven names in accordance with methods recommended by IUPAC. The PIN is ‘propan-2-amine’.



Method (1):
propan-2-amine (PIN)

Method (2):
propan-2-ylazane (propan-2-yl is the preferred prefix)
(1-methylethyl)azane
isopropylazane

Method (3):
propan-2-ylamine (propan-2-yl is the preferred prefix)
1-methylethylamine
isopropylamine