Is it permissible to mention the name of a female relative who slapped the questioner in childhood, affecting his ear, to someone who insists on knowing her name, while the questioner fears that doing so would constitute backbiting (gheebah)?

You should not mention the name of your female relative. Mentioning her name will not achieve justice, and you might be the one who is in the wrong. Speaking ill of her is forbidden backbiting (gheebah). Therefore, you did well by not mentioning her name. If what happened to your ear caused harm, it is better to forgive her due to the reward in pardon and forgiveness. Also, speaking about her to people is harmful and useless.