Hal never really came back to life, you know. The Hal that's currently running around the DCU is only a construct given form and thought by the Guardians.
After Hal's spirit was severed from the Spectre, it was thrown beyond the multiverse, into a place where space and time have no meaning, there it drifted for an eternal instant before finally finding its way to a world strangely similar to the one he knew, yet very different. In time, Hal's spirit drifted to an air force base, one of the few places in this new world that was unchanged. There, he found Joseph Danvers, a man who reminded Hal much of his own father. Hal soon became an emotionally involved spectator in the lives of Joseph and his wife Marie. Before long, Hal saw in the young couple an opportunity for a new life, and a chance for redemption.
Some time later, the Danvers were gifted with the birth of a beautiful baby girl. She'd grow up to be quite the tomboy, a decorated air force pilot, and a real pain in her father's ass.
Marie never knew why she named her daughter Carol. Only that something inside of her knew it was somehow fitting. She couldn't have realized that her unborn child had named herself, honoring the great love of a former life.