1. Identify the principal functional group

   The suffix nitrile has higher priority than the amino group, so the parent chain must include the carbon of the $-C\equiv N$ group.

2. Count the carbon atoms in the parent chain

   For nitriles, the carbon of the cyano group is counted as carbon 1.

   The structure corresponds to: $\mathrm{CH_3-CH(NH_2)-CH_2-C\equiv N}$

   Counting from the nitrile carbon:

   • Carbon 1: nitrile carbon $(-C\equiv N)$
   • Carbon 2: $CH_2$
   • Carbon 3: $CH(NH_2)$
   • Carbon 4: $CH_3$

   So the parent chain has 4 carbons $\Rightarrow$ butanenitrile.

3. Locate the amino substituent

   The $-NH_2$ group is on carbon 3.

4. Write the IUPAC name

   Therefore, the IUPAC name is: $\boxed{\text{3-Aminobutanenitrile}}$

5. Check options

   • A: 2-Aminobutanenitrile $\rightarrow$ wrong position of amino group
   • B: 3-Aminopropanenitrile $\rightarrow$ wrong chain length
   • C: 2-Aminopentanenitrile $\rightarrow$ wrong chain length
   • D: 3-Aminobutanenitrile $\rightarrow$ correct

Hence, the correct option is D.