Ying was pregnant with Hope when she and her husband left their home for safety behind Ba Sing Se's walls. She was born just outside the Outer Wall of the city, with Katara providing pivotal assistance.
When Hope was born, the love and togetherness exhibited by her parents inspired Aang to feel hopeful again, as he was trying to bury his feelings of anger and sadness over losing Appa. It was for this reason that Ying gave Hope her unique name.
Hope and her parents successfully made it to Ba Sing Se, but the Fire Nation proceeded to capture the city shortly thereafter. Hope cried in her mother's arms as Fire Nation soldiers marched through the city.
According to Avatar Extras for "The Serpents Pass", her name was originally going to be "Xi Wang" (希望), meaning "hope" in Chinese, but it was later changed. The creators stated in a DVD commentary for "The Serpent's Pass" episode that this change was meant to help viewers not familiar with Chinese understand the name's meaning.