In the complex \([Co(en)_2Br_2]Br\), where \(en = ethylenediamine = NH_2CH_2CH_2NH_2\), the ligands are:
- 2 bidentate ethylenediamine ligands
- 2 bromide ligands
Since the coordination number is 6, cobalt is in +3 oxidation state.
The naming order:
- Neutral ligands (ethylenediamine)
- Anionic ligands (bromide)
- Metal name with oxidation state
Hence, the correct IUPAC name is:
\[
\text{Dibromo bis (ethylenediamine) cobalt (III) bromide}
\]