You could do this with a trigger, by logging the login + query executed
Create the logging table
CREATE TABLE DBO.SynonymTriggerLogging( ID int Identity(1,1) PRIMARY KEY NOT NULL,
LoginName varchar(200),
QueryExecuted varchar(max));
Create the trigger (If you only want to log login name + the drop statement)
CREATE TRIGGER SynonymTrigger
ON DATABASE
AFTER DROP_SYNONYM
AS
INSERT INTO DBO.SynonymTriggerLogging(LoginName,QueryExecuted)
SELECT ORIGINAL_LOGIN(),EVENTDATA().value('(/EVENT_INSTANCE/TSQLCommand/CommandText)[1]','nvarchar(max)');
Testing
CREATE SYNONYM TEST
FOR dbo.test;
DROP SYNONYM TEST;
Result
SELECT *
FROM DBO.SynonymTriggerLogging;
ID LoginName QueryExecuted
1 rvertongen DROP SYNONYM TEST
If you also need the hostname, use the following table & trigger
CREATE TABLE DBO.SynonymTriggerLogging( ID int Identity(1,1) PRIMARY KEY NOT NULL,
LoginName varchar(200),
QueryExecuted varchar(max),
HostName varchar(200));
GO
CREATE TRIGGER SynonymTrigger
ON DATABASE
FOR DROP_SYNONYM
AS
INSERT INTO DBO.SynonymTriggerLogging(LoginName,QueryExecuted,HostName)
SELECT ORIGINAL_LOGIN(),EVENTDATA().value('(/EVENT_INSTANCE/TSQLCommand/CommandText)[1]','nvarchar(max)'),HOST_NAME()
Also take a look at example D from this link to prevent SYNONYM's from being dropped.