Step 1: To name the coordination compound
\[
[\text{Co(NH}_3)_4(\text{H}_2\text{O})\text{Cl}]Cl_2
\]
we first identify the ligands and their respective prefixes. In this case, we have:
- \( \text{NH}_3 \) (ammine) as the ligand (prefix: tetra- because there are four ammonia molecules),
- \( \text{H}_2\text{O} \) (aqua) as the ligand (prefix: aqua),
- \( \text{Cl} \) (chlorido) as the ligand (prefix: chlorido).
Step 2: Next, we identify the metal ion and its oxidation state. The central metal is cobalt (Co), and the oxidation state is determined by the charges of the ligands:
- The ammine ligands are neutral,
- The aqua ligand is neutral,
- The chloride anion has a charge of -1.
Since the total charge of the complex is neutral (because it is paired with two chloride counterions \( \text{Cl}^- \)), we deduce that the oxidation state of cobalt is \( +3 \). Therefore, the metal is \( \text{Co}^{3+} \).
Step 3: The name of the coordination compound follows the order of naming ligands first, then the metal with its oxidation state in parentheses. The final part of the name refers to the counterions, which in this case are two chloride ions.
Thus, the correct IUPAC name is:
"Tetraammineaquachloridocobalt(III) chloride."
Thus, the correct answer is option (A).