I was having serious reservations about using @@identity, because it can return the wrong answer.
But there is a workaround to force @@identity to have the scope_identity() value.
Just for completeness, first I'll list a couple of other workarounds for this problem I've seen on the web:
Make the trigger return a rowset. Then, in a wrapper SP that performs the insert, do INSERT Table1 EXEC sp_ExecuteSQL ...
to yet another table. Then scope_identity() will work. This is messy because it requires dynamic SQL which is a pain. Also, be aware that dynamic SQL runs under the permissions of the user calling the SP rather than the permissions of the owner of the SP. If the original client could insert to the table, he should still have that permission, just know that you could run into problems if you deny permission to insert directly to the table.
If there is another candidate key, get the identity of the inserted row(s) using those keys. For example, if Name has a unique index on it, then you can insert, then select the (max for multiple rows) ID from the table you just inserted to using Name. While this may have concurrency problems if another session deletes the row you just inserted, it's no worse than in the original situation if someone deleted your row before the application could use it.
Now, here's how to definitively make your trigger safe for @@Identity to return the correct value, even if your SP or another trigger inserts to an identity-bearing table after the main insert.
Also, please put comments in your code about what you are doing and why so that future visitors to the trigger don't break things or waste time trying to figure it out.
CREATE TRIGGER TR_MyTable_I ON MyTable INSTEAD OF INSERT
AS
SET NOCOUNT ON
DECLARE @MyTableID int
INSERT MyTable (Name, SystemUser)
SELECT I.Name, System_User
FROM Inserted
SET @MyTableID = Scope_Identity()
INSERT AuditTable (SystemUser, Notes)
SELECT SystemUser, 'Added Name ' + I.Name
FROM Inserted
-- The following statement MUST be last in this trigger. It resets @@Identity
-- to be the same as the earlier Scope_Identity() value.
SELECT MyTableID INTO #Trash FROM MyTable WHERE MyTableID = @MyTableID
Normally, the extra insert to the audit table would break everything, because since it has an identity column, then @@Identity will return that value instead of the one from the insertion to MyTable. However, the final select creates a new @@Identity value that is the correct one, based on the Scope_Identity() that we saved from earlier. This also proofs it against any possible additional AFTER trigger on the MyTable table.
Update:
I just noticed that an INSTEAD OF trigger isn't necessary here. This does everything you were looking for:
CREATE TRIGGER dbo.TR_Payments_Insert ON dbo.Payment FOR INSERT
AS
SET NOCOUNT ON;
IF EXISTS (
SELECT 1
FROM
Inserted I
INNER JOIN dbo.Payment P ON I.CustomerID = P.CustomerID
WHERE
I.DateFrom < P.DateTo
AND P.DateFrom < I.DateTo
) ROLLBACK TRAN;
This of course allows scope_identity() to keep working. The only drawback is that a rolled-back insert on an identity table does consume the identity values used (the identity value is still incremented by the number of rows in the insert attempt).
I've been staring at this for a few minutes and don't have absolute certainty right now, but I think this preserves the meaning of an inclusive start time and an exclusive end time. If the end time was inclusive (which would be odd to me) then the comparisons would need to use <= instead of <.