For example: "I could tell he had had a great time at the circus."
If you're not repeating the word for emphasis, is there a term for the sequential usage, other than "coincidence"?
You might call this a homonymic phrase (or compound).
Since homonyms are words that sound the same (or are spelled the same) this might be a proper term do describe a phrase, or a part of a phrase, that includes them.
Reading through the closest article to the subject, that I could find in wikipedia did not reveal any specific terms that would cover this scenario.
There are plenty of contrived sentences allowing anything up to an infinite number of repetitions, but no-one has actually given an example where repeating a word serves to emphasise anything. So how about...
Okay, maybe not the best example. But I do think it conveys emphasis.