It occurs to me that our organization and developers need a better method to monitor modifications on specific objects, either DDL or DML, when then might affect "custom" or "one off" objects.
In the (unlikely) event that you're interested only in the downstream impact of changes which do not transcend your SQL database, the following may be of some use to you:
SELECT
referencing_schema_name,
referencing_entity_name,
referencing_id,
referencing_class_desc,
is_caller_dependent
FROM sys.dm_sql_referencing_entities ('<object_name>', 'OBJECT');
GO
Bear in mind that impact analysis is a fundamental part of maintenance and Change Control and needs buy in from everyone to be effective. The work and effort involved in achieving a good mechanism is typically substantial (and costly) so needs to be balanced against the benefits of implementing it. Obviously the above snippet will not highlight the impact to items outside your database(s) so, if that constitutes a significant portion of your solution, you should probably start thinking about a lineage-impact model.