IUPAC Name of Substituted Benzonitrile Derivative

To determine the IUPAC name of the given compound, we follow the standard IUPAC nomenclature rules:

1. Identification of the Principal Functional Group:
   The compound contains three functional groups:

   • Nitrile ($-\text{CN}$)
   • Alcohol ($-\text{OH}$)
   • Halogen ($-\text{Br}$)

   According to the IUPAC priority order of functional groups:
   $\text{Nitrile } (-\text{CN}) > \text{Alcohol } (-\text{OH}) > \text{Halogen } (-\text{Br})$
   Therefore, the principal functional group is the nitrile group ($-\text{CN}$), and the parent compound is benzonitrile.

2. Numbering the Ring:

   • The ring carbon attached to the principal functional group ($-\text{CN}$) is assigned position $1$.
   • The ring substituents are a bromo group ($-\text{Br}$) adjacent to the nitrile carbon, and a hydroxy group ($-\text{OH}$) located para to the bromo group.
   • We number the ring to give the lowest locant set at the first point of difference:
     • Numbering clockwise (towards the $-\text{Br}$ substituent):
       $\text{C-1: } -\text{CN}, \quad \text{C-2: } -\text{Br}, \quad \text{C-5: } -\text{OH} \implies \text{Locant set: } (2, 5)$
     • Numbering counter-clockwise:
       $\text{C-1: } -\text{CN}, \quad \text{C-3: } -\text{OH}, \quad \text{C-6: } -\text{Br} \implies \text{Locant set: } (3, 6)$
   • Comparing the sets at the first point of difference, $2 < 3$, so the correct numbering assigns locant $2$ to bromine and locant $5$ to the hydroxy group.

3. Alphabetical Ordering of Substituents:

   • The substituents as prefixes are "bromo" and "hydroxy".
   • Alphabetically, "bromo" precedes "hydroxy".

Combining the prefixes with the parent name gives:
$\text{2-Bromo-5-hydroxybenzonitrile}$

Therefore, the correct option is B.