Sql server Database instance with SQL Authentication

Hello,
I am trying to create a testing. Database1 instance of a database with SQL Authentication which was previously set on Windows Authentication and  dbo.
I have a Audit trial set on the StoredProcedures .
 The Audit Trial table (Table_Debug) has credential susername.

Query used in the Stored Procedure is
Insert into Table_Debug(sql)
After execution of the above query the entry in the table is like:

Table_Debug

SQL                                                Username  
"Select * from table1"                 "Network\Username"

Now after setting as the new database instance as  testing. Database1

The above query gives result as

SQL                                                Username  
"Select * from table1"                 "testing.Database1"


Any suggestion on how to get the user name who is connected to the Database.
Any change I can do on the credentials of the table.

Cheers