How to synonymize a database name?
OK, I managed to solve this by creating a Synonym in DBApp_DEV:

CREATE SYNONYM GenTableName FOR DBGen_DEV.dbo.TableName


And in DBApp_QA, the Synonym would be:

CREATE SYNONYM GenTableName FOR DBGen_QA.dbo.TableName


This way, I can maintain the exact same query in my SP that exists in both DBApp_* databases:

select Col1 from GenTableName