Step 1: Recall the carbylamine reaction.
In the carbylamine reaction, a primary amine (R–NH$_2$) reacts with chloroform (CHCl$_3$) and alcoholic KOH to form isocyanides (R–NC), which have a foul smell.
Step 2: Match with the given reaction.
The given equation:
\[
R–NH_{2} + CHCl_{3} + 3KOH \longrightarrow RNC + 3KCl + 3H_{2}O
\]
fits exactly with the carbylamine test.
Step 3: Analyzing options.
- (A) Coupling reaction: Involves diazonium salts, not applicable here.
- (B) Carbylamine reaction: Correct. Forms isocyanides (R–NC).
- (C) Hoffmann bromamide reaction: Converts amides to amines, not relevant here.
- (D) Schmidt reaction: Reaction of hydrazoic acid with carboxylic acids, different case.
Step 4: Conclusion.
Therefore, the given reaction is the carbylamine reaction.
Final Answer:
\[
\boxed{\text{(B) Carbylamine reaction}}
\]