The correct IUPAC nomenclature for the following compound is:

IUPAC name of the following compound is

$2$-Methyl-$5$-oxo-hexanoic acid

1. Identify the longest continuous carbon chain that contains the carboxyl group ($\mathrm{COOH}$). In this case, it is a six-carbon chain.

2. Number the carbon chain starting from the end closest to the carboxyl group. The carboxyl carbon is assigned the number $1$.

3. Identify and name any substituents attached to the carbon chain. In this case, there is a methyl group attached to the second carbon atom of the chain.

4. Combine the substituent name with the parent chain name, with a hyphen in between. The resulting name is "2-methylhexanoic acid".

5. Finally, add the prefix "oxo" to indicate the presence of a ketone group ($\mathrm{C}=\mathrm{O}$) on the fifth carbon of the chain.