Death is the Great Shape-Changer for two reasons. First, Dustfinger implies that this is not because Death can change their own form, but rather because death changes the forms of others:
They came to Silvertongue more often than to Dustfinger himself, as if to make sure that the Bluejay didn’t forget the bargain he had struck with their mistress, the Great Shape-Changer who made all things wither and blossom, grow and decay.
Withering, blossoming, growth and decay are processes that alter the forms of objects and creatures, changing their shapes. In other words, Death is change: for something new to come into being, something old must die, whether literally, such as flowers dying and their remains feeding new plants, or somewhat more metaphorically, a child fading away as they grow to adulthood. Death represents metamorphosis, and that is why Death becomes a butterfly and a caterpillar: the death of the caterpillar is the birth of the butterfly.
As Death says:
“I am the beginning of all stories, and their end,” it said in the voice of the bird, in the voice of the squirrel. “I am transience and renewal. Without me nothing is born, because without me nothing dies.
However, Death is also the Great Shape-Changer because they appear in many different forms, whether from a metafictional perspective (Death is portrayed in different ways in different stories) or from a more mundane one: living creatures can die in many different ways:
“All stories end with me, Bluejay,” Death said. “You will find me everywhere.” And as if to prove it, the marten turned into the one-eared cat that liked to steal into Elinor’s garden to hunt her birds.
Mortimer perceives Death as an old woman who takes the form of animals.
“As you see, my daughters don’t like to let him go,” said the old woman’s voice. “Even though they know he will come back.”
But this is probably just how Death seems to him:
But the marten laughed. And once again it sounded [emphasis mine] like an old woman’s laughter.
(Or possibly how Death manifests to those coming from the world of Inkheart, since Dustfinger also sees her that way.)
Orpheus seems to think of Death as a powerful father figure:
“Hear me, Master of the Cold,” said the poet. “Hear me, Master of Silence. I offer you a bargain. I send you the Bluejay, who has made mock of you. He will believe that he has only to call on your pale daughters, but I am offering him to you as the price for the FireDancer.
However, Death is none of these things and all of them. Death is no more and no less a powerful lord than a tired old grandmother, no more and less than a cat, a pine marten, or a bird.