The civilized term for a Franken-backing is a Pieced Backing. It is an accidental opportunity to create a secondary work of art. I lay out my scraps and look at them like a jigsaw puzzle. How do I combine these to make enough fabric to equal the size of backing I need?
It takes a bit of time, but once you put the jigsaw together, you end up with a thrifty work of likely modern art! What a great way to use leftover fabric and have a one-of-a-kind backing for your quilt.