There may be a day when Kara Zor-El is ready to leave the Supergirl mantle behind for good, but an upgrade to 'Superwoman' might not be that easy. Despite it being the most obvious choice, the Superwoman mantle has quite a dark history unbefitting of a hero like Kara.
After she survived Krypton's destruction and eventually made her way to Earth, Kara discovered that her baby cousin was now a full-grown man and the planet's number one protector. Like Superman, Kara developed powers thanks to the yellow rays of the sun and she became a hero just like Clark. Supergirl and Superman protected Earth together for years, and what started as two Kryptonian heroes eventually grew into an entire family. In that time, Supergirl has seen others take on new identities as they got older, such as when Jon Kent abandoned the Superboy title to take on the name Superman in record time.
But if Kara's been around for as long as she has, why is she still going by Supergirl and not Superwoman, a more age-appropriate name? As it turns out, that name has some particularly dark baggage. That fact came to light in Supergirl #40 by Sterling Gates and Jamal Igle. After the Bottle City of Kandor was resurrected, Kara came into contact with a powerful woman who wore the Super Family's "S" shield and called herself Superwoman. Though Kara is unsure of the stranger's identity, the stresses of the mounting tensions between Earth and New Krypton cause Supergirl to confide in Superwoman. However, unbeknownst to Kara, Superwoman is actually Major Lucy Lane (Lois Lane's younger sister) who has been acting on her father, General Sam Lane's, orders as part of his plans to neutralize the Kryptonian threat. As Superwoman, Lucy used her powers willingly to kill innocent people as part of the operation.
Of course, Lucy isn’t the first evil Superwoman. Before Lois Lane's sister ever tried on the mantle, a woman named Dana Dearden christened herself as Superwoman in a bid to win the Man of Steel's favor, only to turn when her feelings weren't reciprocated. But perhaps the most well known use of the Superwoman name belongs to the Earth-3 counterpart of Wonder Woman, who's proven to be just as bad as Diana is righteous.
Needless to say there's a pretty checkered past with the Superwoman name. Although Kara does take on the identity in DC’s Future State, it doesn’t change the dark history associated with the mantle. While Superwoman is a good future name for Supergirl, the name has an unfortunate toxicity tacked onto it. People like Lucy Lane and the Earth-3 villain took the noble "Super" prefix and used it to commit some heinous acts that no one bearing the House of El symbol would ever do. It's unfortunate that Kara has essentially been robbed of her natural progression just because certain villains got to the name first. But she deserves a better identity, one that hasn't been shared with evildoers. In a perfect world, Supergirl would be able to become Superwoman, but too many bad apples have spoiled the name for her.