The complex is:
\[
[Co(NH_3)_5ONO]Cl_2
\]
Outside the bracket there are 2 chloride ions, so the complex cation has charge \(+2\).
Now calculate oxidation state of cobalt:
\[
x + 0 + (-1)=+2
\]
\[
x-1=2
\Rightarrow x=+3
\]
So cobalt is in the +3 oxidation state.
The ligand \(ONO\) is nitrito.
Thus the name is:
\[
\text{Pentaamminenitritocobalt (III) chloride}
\]
Hence, the correct answer is:
\[
\boxed{(A)}
\]