Instead of inventing the word "beginnator" as the opposite of terminator, how about "initiator"? It's already an English word. Statement initiator vs. statement terminator--I think that sounds reasonable.
I've seen some confusion as to what constitutes a statement in T-SQL. For example, I've seen this:
BEGIN TRY;
-- try block
END TRY
BEGIN CATCH;
-- catch block
END CATCH;
There is no semi-colon after END TRY because the parser doesn't allow it. The semi-colons after BEGIN TRY and BEGIN CATCH are empty statements, not statement terminators. Both BEGIN constructs are opening a scope.
Note that WITH doesn't require a semi-colon on the previous statement if it's the first statement in its scope.
CREATE PROC try_test AS
DECLARE @i INT = 2 -- missing a semi colon
BEGIN TRY
WITH x AS (SELECT @i AS y)
SELECT *
FROM x;
END TRY
BEGIN CATCH
-- do nothing
END CATCH;
GO
EXEC try_test;
GO
DROP PROC try_test;
Of course, you don't want to rely on the beginning of a scope. That declaration should have a semi-colon terminator. But I'm getting tired of seeing "terminators" on BEGIN constructs.