Step 1: Approach
Recall the name reaction and its conditions.
Step 2: Key points
The Finkelstein reaction is an $\text{S}_\text{N}2$ halide exchange. The iodide ion is the nucleophile, so we need a soluble source of $\text{I}^-$, which is sodium iodide. The solvent is dry acetone because it dissolves NaI but not NaCl or NaBr.
Step 3: Result
The precipitate of NaCl or NaBr drives the reaction forward (Le Chatelier). So the reagent is NaI in dry acetone, option (B).
Final Answer:
The Finkelstein reaction uses NaI in dry acetone, option (B).
\[ \boxed{\text{NaI in dry acetone}} \]