Well, mentioning the plural brings a new perspective...

For me designing and naming a good API is far more complicated than coding, since it involves human psychology.

Especially since sometimes good names are already used or even only reserved.

This brings a new concern, wasting an otherwise better used word.

overlaps could mean much more things and especially in plural it could indicate tuples bigger than just a pair of values.

The English grammar has no dualis alongside singular and plural like for instance Arabic, so only constructs like pair or couple indicate 2 tuples, and couples are normally disjoint. Maybe a construct with prefix "bi-" could solve this (think bigamie ;-)

Other than describing the tuple as a whole one could try describing the relation between two elements.

So my best guess ATM is "neighbor" but in singular(!). The neighbor can't mean anything else it describes a relation between 2 objects.

Words like next or link already have different meaning and bichain sounds artificial in my ears.¹

Otherwise I would consider successor or one of the synonyms like follower or one of it's synonyms like companion.

As soon as the definition is clear seeking through a thesaurus is of help.

updates

¹) bimap ?