Oh! "Clippy bit" is a great name.

Much better than "Plate 1x1 W. Up Right Holder," and much better than "you know -- one that goes here and holds up the other one?" In other words:

So I was looking for a picture... and I came across Bricklink -- which I never knew existed.

Following up on the Lego house: it is finished, but with an unfortunate ending.