Identify the parent functional group

The compound is a substituted benzoic acid, since the principal functional group is the carboxylic acid group, $-COOH$.

Therefore, the parent name is: $\text{benzoic acid}$

Assign numbering on the benzene ring

In benzoic acid, the carbon attached to $-COOH$ is taken as position $1$.

Number the ring so that the substituents get the lowest possible set of locants.

From the given structure, the substituents are:

• $-OH$ at position $2$
• $-Br$ at position $3$
• $-NO_2$ at position $5$

So the locants are: $2\text{-hydroxy},\ 3\text{-bromo},\ 5\text{-nitro}$

Arrange substituents in alphabetical order

Prefixes must be written in alphabetical order:

• bromo
• hydroxy
• nitro

Hence the name becomes: $\text{3-Bromo-2-hydroxy-5-nitrobenzoic acid}$

Check the options

• A: $\text{3-Bromo-2-hydroxy-5-nitrobenzoic acid}$ ✅ Correct
• B: $\text{2-Hydroxy-3-bromo-5-nitrobenzoic acid}$ ❌ Same locants, but substituents are not arranged alphabetically
• C: $\text{3-Bromo-4-hydroxy-1-nitrobenzoic acid}$ ❌ Incorrect numbering and parent naming
• D: $\text{5-Nitro-3-bromo-2-hydroxybenzoic acid}$ ❌ Substituents not in alphabetical order

Final answer

The correct IUPAC name is: $\boxed{\text{3-Bromo-2-hydroxy-5-nitrobenzoic acid}}$