Step 1: Identify the parent chain.
The longest chain contains 3 carbons \(\Rightarrow\) propane is the parent chain.
Step 2: Locate substituents.
- A bromo group is attached at carbon 2.
- A methyl group is also attached at carbon 2.
Step 3: Apply IUPAC rules.
The name becomes \(\mathrm{2-bromo-2-methylpropane}\).
Step 4: Check incorrect options.
(A) Tertiary butyl chloride: Wrong halogen.
(B) Secondary butyl chloride: Incorrect structure.
(C) 2-bromo-2-methyl propane: Correct IUPAC name.
(D) 2,2-dimethyl-1-bromoethane: Incorrect naming.
Step 5: Conclusion.
Thus, the correct name is (C) 2-bromo-2-methyl propane.