Finding all functions/stored procedures that reference a certain procedure/function?
sys.sql_expression_dependencies should give you what you want if you don't want to search through the definition of every single object (especially when references may or may not have schema prefixes).

I think you can get what you want with the following query:

SELECT 
    o.name AS ReferencingObject, 
    sd.referenced_entity_name AS ReferencedObject
FROM sys.sql_expression_dependencies  AS sd
INNER JOIN sys.objects AS o
    ON o.object_id = sd.referencing_id
WHERE sd.referenced_entity_name = 'my_object_name';