Update audit database name in triggers and views of main database?
You can use the text column from sys.all_sql_modules to create alter scripts with your new database names. Below is an example where I use AdventureWorks2014 to replace any text where there is a CREATE with an ALTER while changing database name HumanResources to HR.  Again this will only generate your scripts.

EDIT: Replaced syscomments with all_sql_modules.  Thanks Kenneth Fisher!

USE AdventureWorks2014
GO

SELECT 
    o.name,
    o.type,
    o.type_desc,
    sc.definition,
    REPLACE(REPLACE(sc.definition, 'CREATE ', 'ALTER '),'[HumanResources]','[HR]')
FROM sys.all_sql_modules sc
    inner join sys.objects o 
        on sc.object_id = o.object_id
WHERE o.type IN ('V','TF','P','TR') --Views, Table Function, Proc, Trigger. You can include/exclude additional types if you choose.


Hope this helps!