Step 1: Identify the principal functional group.
The compound contains several functional groups: nitrile (-CN), ketone (-C=O), hydroxyl (-OH), amine (-NH\(_2\)), and bromo (-Br).
According to the IUPAC order of priority, the nitrile group (-CN) has the highest priority among these. Therefore, the compound is named as a nitrile, and the carbon of the -CN group is numbered as C1.
Step 2: Identify and number the parent chain.
The parent chain is the longest carbon chain that includes the principal functional group. Starting from the nitrile carbon as C1, we number the chain.
\( \text{N}\equiv\text{C}_1-\text{C}_2(\text{Br})-\text{C}_3(=\text{O})-\text{C}_4-\text{C}_5(\text{OH})-\text{C}_6(\text{NH}_2) \)
The longest chain has 6 carbon atoms. Therefore, the parent alkane is hexane, and the parent name is hexanenitrile.
Step 3: Identify and name the substituents.
We have the following substituents at their respective positions:
- At C2: a bromo group. Name: 2-bromo.
- At C3: a ketone group. When a ketone is a substituent, it is named "oxo". Name: 3-oxo.
- At C5: a hydroxyl group. When a hydroxyl is a substituent, it is named "hydroxy". Name: 5-hydroxy.
- At C6: an amine group. When an amine is a substituent, it is named "amino". Name: 6-amino.
Step 4: Assemble the full IUPAC name.
The substituents are listed in alphabetical order (Amino, Bromo, Hydroxy, Oxo).
The full name is: 6-Amino-2-bromo-5-hydroxy-3-oxohexanenitrile.
This matches option (C).