From inside a SQLCLR trigger we have access to the action performed, the (windows) user performing the action, column count and the affected columns through the SqlContext.TriggerContext. But the object that was affected is inaccessible. Please provide us also the parent object that was affected by the action. Adding a single int property "ParentID", holding the object_id for the trigger's parent object is sufficient for the purpose.
Erland Sommarskog has already requested the same functionality back in 2006, but his request was for @@procID to be adapted for the purpose. His request was rejected on grounds of the designed functionality of @@procID (https://connect.microsoft.com/SQLServer/feedback/details/126461/-procid-returns-invalid-id-when-called-by-a-net-dml-trigger#tabs). The functionality he requested is however still very much needed. A quick search on the internet shows many more people need this, for example for creating a generic auditing trigger. There currently is no known alternative way to make one generic SQLCLR trigger assembly that is registered as a trigger on multiple objects in SQL server. In a T-SQL trigger this information is never needed, because you can not implement a T-SQL trigger that fires on multiple objects, i.e. the parent object is always known. But a SQLCLR trigger CAN be registered on multiple objects at the same time, i.e. here we do need to be given the parent object.