Am I obligated to repay the sheep my mother lent me to name my daughter with, knowing that she passed away before the Eid on which I agreed with her to return it, and is it permissible for me to eat from it or give it all away in charity?

The mother's intention to slaughter a sheep on Eid does not make it an udhiyah (definition) (sacrificial animal) according to the majority of scholars, unless she designates it explicitly with words. If the sheep becomes an udhiyah, then nothing is permissible to do with it other than slaughtering it. If it is sold or lent, then the proceeds must be given in charity. However, if it was not an udhiyah, then it is permissible for the mother to lend it. If the mother passes away before the loan is repaid, it is considered a debt owed by you and is part of her estate to be divided among the heirs.