emily is the name of characters that are rescued in bioshock infinite as well as the first dishonored game. both games are around a decade old but were popular at the time.
Isn't the character in Bioshock Infinite 'Elizabeth'? I'd also assert that by design, Elizabeth was meant to be a character that arguably didn't really need to be rescued, "she can take care of herself".
The only name I could think of in 5 letters that fit here was actually "Peach".