Step 1: Understanding the Question:
We need to determine the correct nomenclature for isobutyl alcohol using the older, common carbinol system of naming alcohols.
Step 2: Detailed Explanation:
In the carbinol naming system, the simplest alcohol molecule, methanol ($\text{CH}_3\text{OH}$), is given the foundational base name 'carbinol'.
The specific carbon atom directly attached to the hydroxyl (-OH) group is referred to as the carbinol carbon. Any alkyl groups attached to this specific carbinol carbon are treated as substituents and named first.
Let us write out the structural formula of isobutyl alcohol:
$$(\text{CH}_3)_2\text{CH}-\text{CH}_2-\text{OH}$$
In this structure, the terminal $\text{-CH}_2\text{OH}$ unit acts as the base 'carbinol' core.
The remaining alkyl group attached directly to this carbinol core is $(\text{CH}_3)_2\text{CH}-$.
This specific branched three-carbon group is structurally known as an isopropyl group.
Therefore, by linking the substituent name to the base name, we get 'isopropyl carbinol'.
Step 3: Final Answer:
The name of the compound in the carbinol system is Isopropyl carbinol, matching option (C).