Name of dramaturgical device where one interrupts oneself

I'm looking for an English word, if one exists, that describes a pattern of repetition—like epanalepsis, but where an actor interrupts him or herself in between repetitions. Example:

“Send the communique, absolutely. There's a Bahrain Agreement that says... send [the communique].”

— The West Wing "Swiss Diplomacy" by Eli Attie & Kevin Falls

Does any word for this exist?

The word you're looking for is anacoluthon. From Sylvae Rhetorica:

anacoluthon A grammatical interruption or lack of implied sequence within a sentence.

That is, beginning a sentence in a way that implies a certain logical resolution, but concluding it differently than the grammar leads one to expect. Anacoluthon can be either a grammatical fault or a stylistic virtue, depending on its use. In either case, it is an interruption or a verbal lack of symmetry. Anacolouthon is characteristic of spoken language or interior thought, and thus suggests those domains when it occurs in writing.

Not to be confused with metanoia, which is explicitly correcting oneself after starting out on a different tack. See this answer on Writers.