Step-by-Step Solution:

1. Identify the Functional Groups: The given compound is a substituted benzene ring. The substituents are:

   • -CN (cyano group)
   • -OH (hydroxyl group)
   • -Br (bromo group)

2. Determine the Principal Functional Group: According to the IUPAC rules for nomenclature of polyfunctional compounds, we must determine the principal functional group based on the priority order. The priority order for the relevant groups is: Nitrile (-CN) > Alcohol/Phenol (-OH) > Halo (-Br) Therefore, the cyano group (-CN) is the principal functional group. This means the parent name of the compound will be derived from the nitrile.

3. Identify the Parent Compound: Since the principal functional group -CN is attached to a benzene ring, the parent compound is benzonitrile.

4. Number the Carbon Atoms of the Benzene Ring: The carbon atom of the benzene ring attached to the principal functional group (-CN) is assigned the number 1. We then number the ring to give the lowest possible locants to the other substituents (-Br and -OH). There are two possible numbering schemes:

   • Path A (Clockwise): The -Br group is at position 2, and the -OH group is at position 5. The locant set is (1, 2, 5).
   • Path B (Counter-clockwise): The -OH group is at position 3, and the -Br group is at position 6. The locant set is (1, 3, 6).

5. Apply the Lowest Locant Rule: We compare the two locant sets (1, 2, 5) and (1, 3, 6). At the first point of difference, 2 is lower than 3. Therefore, the correct numbering scheme is Path A, which gives the locant set (1, 2, 5).

   • C1: attached to -CN
   • C2: attached to -Br (Bromo)
   • C5: attached to -OH (Hydroxy)

6. Assemble the IUPAC Name: The substituents are listed in alphabetical order before the parent name. The substituents are Bromo and Hydroxy.

   • Alphabetical order: Bromo comes before Hydroxy.
   • The name is constructed as: [locant for bromo]-[Bromo]-[locant for hydroxy]-[hydroxy][parent name]
   • Substituting the values: 2-Bromo-5-hydroxybenzonitrile.

7. Evaluate the Given Options:

   • A: 4-Bromo-3-cyanophenol: Incorrect. This name treats -OH as the principal functional group, which has lower priority than -CN.
   • B: 2-Bromo-5-hydroxybenzonitrile: Correct. This matches our derived IUPAC name.
   • C: 2-Cyano-4-hydroxybromobenzene: Incorrect. This treats -Br as the basis for the parent name, which has the lowest priority of the three functional groups.
   • D: 6-Bromo-3-hydroxybenzonitrile: Incorrect. This uses the wrong numbering scheme (counter-clockwise), which does not follow the lowest locant rule.

Therefore, the correct IUPAC name for the given compound is 2-Bromo-5-hydroxybenzonitrile.