Step 1: Hydrogenation reaction.
When aromatic aldehydes like benzaldehyde react with ammonia in the presence of hydrogen and nickel, they undergo reduction to form the corresponding amine. In this case, the product formed is phenylethylamine.
Step 2: Conclusion.
Thus, the correct product is phenylethylamine \( C_6H_5CH_2NH_2 \), so the correct answer is option (C).
Final Answer:
\[
\boxed{\text{(C) } C_6H_5CH_2NH_2}
\]