To solve this question, we need to understand the coordination chemistry of cobalt (III) complexes and the behavior of chloride ions within these complexes.
Based on the analysis, the complex which will not give a test for chloride ions with silver nitrate is CoCl_3\cdot 3NH_3.
The IUPAC name for the complex \( [\text{Co}(\text{ONO})(\text{NH}_3)_5]\text{Cl}_2 \) is