adjoin seems too similar to join ...

That's kind of why I liked it.

... which is unrelated.

join intersperses adjacent elements of a list with something.

This (in the simple 2 at a time variant) is often used to add adjacent elements of a list together -- ad-join.

A vote for overlaps (BTW, wouldn't "overlaps" be enough?).

Um. I thought about that, and still haven't reached a conclusion which is better.

In the singular, it sort of implies something only happens once.

But if you read 'overlaps' as a plural as in "there are many overlaps"; rather than the (*)???: "it overlaps", then it makes more sense I think.

Not sure what grammatical term applies here?

The nice thing about overlap(s) is it works for the variable width (depth?) of overlap also which adjoin doesn't.

I think I'm beginning to favour overlap(s) also.

But now I'm also thinking about overmap and mapover?