Step 1: Identify the parent chain.
The compound has three carbons with a carboxylic acid group \((-COOH)\) \(\Rightarrow\) parent acid is propanoic acid.
Step 2: Locate and name the substituent.
There is an \(-OH\) (hydroxy) substituent on the second carbon: \(\mathrm{CH_3\!-\!CH(OH)\!-\!COOH}\).
Step 3: Write the IUPAC name.
Position + substituent + parent: \(\boxed{\text{2-hydroxypropanoic acid}}\).
Step 4: Conclusion.
Hence, the correct option is (B).