It should be called relationing but that would terrible. Coupling makes more sense even.
Coupling would only work with romantic shipping at the end of the day. I get that "two characters" are "a couple of characters", but when I hear couple in that context, I think romantic couple.
Relationing kind of works, but it may make people think of when you pair characters together as "fake family", which is a type of shipping (basically when the characters are so close, they're practically family - father/mother figures, or brother/sister figures).
We have derailed.