Term for wordplay using adjacent repetition of homophones

Jim Wegryn calls it a dittogram.

This wikipedia entry refers to them as "alliterations".

It uses one of my favorite limeriks as an example (note that 4:04 is spoken as 'four-four'):

There's a train at 4:04 said Miss Jenny. 
Four tickets I'll take. Have you any? 
Said the man at the door. "Not four for 4:04, 
For four for 4:04 is too many."

However, "alliteration" is a broader term which can apply to repeated syllables and sounds, and not just complete words.

Maybe there isn't a specific word for what you're describing, but you can hone it down to a phrase: "homophones used for alliteration".

There is no special term. Alliteration focuses on initial sounds (the graveyard 'Peace, perfect peace') while rhyme is about endings (stressed syllable onward e.g. Nash's 'rhinocerous - prepocerous'). Consonance is about consonants (the c-v-c syllables 'live, love') and assonance about nearby vowel sounds ('high rise'). A published example of mine achieves 11 homophone repetitions, and is entirely plausible teaching (especially for philosophy students, poor things).

We are here, but for others distant we are 'over there', so our 'here' is their 'there'.
Please don't cry. We are here, but I see you writhe ere 'their there'. There, there — they're there! Their 'there' they're therefore seeing as over here.
That's it really. Let's celebrate, cohere. Hear here 'Hear, hear!' Here, heroes all, ends the lesson, succinctly.