Is there a character in any mythology or folklore that was notable for having created themselves?
This might be a lot more common than you'd think. Many examples come from creation myths, perhaps because having a creator at all begs the obvious question, "who created the creator?" One solution is to declare the creator eternal. The other is a self-created deity.
For instance, the creator god in ǃKung mythology called ≠Gao!na:
≠Gao!na created himself; then he created a lsser god and wives for himself and the lesser god. He named himself Hishe (The One Whom No One Can Command) and gave names to his own wife and to the lesser god and his wife.
Lynch, Patricia Ann, and Jeremy Roberts. African Mythology, A to Z. Infobase Publishing, 2010.
In the Ancient Egyptian creation myth, Atum is also described as having created himself.
In the beginning were the primeval waters, named Nun, which, since they were unconscious and inanimate, were incapable of independent action. Out of the waters Ra raised himself on a hill and created himself . . . For reasons that remain obscure to mortals, he conceived the idea of creation and willed his own physical existence.
Armour, Robert A., and Alison Baker. Gods and Myths of Ancient Egypt. Cairo: American University in Cairo Press, 1986.
He then fertilised himself by giving himself oral sex and produced the twins Tefnut and Schu.
In some versions of ancient Indian creation myth, the creator god Brahma is described as self created:
Brahama came to him and said, "Tell me, who are you?" Vishnu replied, "I am Vishnu, creator of the unvierse, All the worlds, and you yourself, are inside me. And who are you?" Brahma replied, "I am the creator, self-created, and everything is inside me."
Doniger, Wendy. The implied spider: Politics and theology in myth. Columbia University Press, 2010.
Other versions describe him as being created by Vishnu or born of the lotus from Vishnu's navel, though.