Step 1: Understand the naming convention.
The IUPAC name for coordination compounds involves naming the ligands first (NH\(_3\) and NO\(_3\)) followed by the metal and its oxidation state.
Step 2: Conclusion.
Thus, the correct IUPAC name is pentamminenitrito-N-cobalt (III) chloride.
Final Answer:
\[
\boxed{D}
\]