The majority of street lights in Hampshire are owned either by Hampshire County Council (HCC) or a local Parish Councils. SSE maintain all to HCC’s street lights under a PFI contract. This contract also includes some local Parish Councils.
You can report faults on units maintained by the PFI contract using the fault reporting tool here
If your light is not featured on the map then it is likely that the street light belongs to a local Parish Council who is not part of the PFI. It may alternatively be privately owned or belong to a housing association. SSE does not maintain these units, and faults should be reported directly to the local Parish Council or company that manages them.