Neither of them is Slytherin's heir. Although, as Dumbledore says,
The Peverells, Gaunts, Blacks, Malfoys, Potters, Weasleys, Prewetts, and other families are all linked to one another through bloodlines and intermarriage. The only known direct descendants from Salazar Slytherin were the Gaunts, who for the most part shared their ancestor's beliefs in the purity of wizard blood.
The "Heir" was the soul-bit of Tom Riddle left behind in the Horcrux diary. Tom was able to gain Ginny Weasley's trust and eventually possessed her.
Her real parents were Daneel and Dean Novak, Pureblooded wizards. Turns out Daneel was Tom Riddles younger sister, Daneel Riddle. Of course, the Riddles were related to Salzar Slytherin himself, and this made Hermione the living heir of Slytherin. The problem with being a female Slytherin heir, is that they're cursed.
Ginny was possessed by the spirit/portion of soul that was inside Tom Riddle's diary/horcrux. This is what enabled her to open the Chamber of Secrets. Tom Riddle was the only known remaining descendant of Salazar Slytherin and a Parselmouth (Parseltongue is the language).
Andrea Deanisi as Wiglaf Sigurdsson, the Heir of Rowena Ravenclaw.
Harry is the Heir of Gryffindor (though his powers have been bound by his father when he was a baby), Neville is the Heir of Hufflepuff, Meghan (OFC, daughter of Sirius) is the Heir of Ravenclaw. Harry/Ginny, Ron/Hermione, Remus/Tonks. Sixth year. After a rare magical illness Harry becomes outstandingly powerful.
Albus ended up in Slytherin because he couldn't stop thinking about ending up in Slytherin, and so the Sorting Hat couldn't grasp anything other than his thoughts about being in Slytherin.
The Heir of Hufflepuff was a person foretold by the Seer Harmonthrep (Ajrand) to bring great glory and honor to the House of Hufflepuff, considered boring and lackluster by most.
He is cunning
Slytherins are a cunning lot, and there are all kinds of examples of Albus Potter using his wiles to come up with schemes and plans worthy of any member of Salazar's house throughout Harry Potter and the Cursed Child.
Bellatrix Lestrange
Bellatrix Lestrange died during the Battle of Hogwarts. Warner Bros. A loyal Death Eater and member of Slytherin House, Bellatrix Lestrange was Sirius and Regulus Black's cousin.
Harry Potter came very close to being sorted into Slytherin before he persuaded the Hat to sort him into Gryffindor. Yet the spectre of Slytherin haunted him for some time afterwards, becoming particularly potent in Harry Potter and the Chamber of Secrets, when he was rumoured to be the heir of Slytherin.
The whole "Lord Voldemort : Heir of Slytherin" seems to have been something that Voldemort concocted on his own, as part of his attempt to rationalise his mixed parentage and to construct a mythos around himself. As such, Dumbledore couldn't have been the first to know that Riddle was styling himself thusly.
Through his mother's family, he is the last descendant of the wizard Salazar Slytherin, one of the four founders of Hogwarts School of Witchcraft and Wizardry.
Ginny Weasley was able to speak Parseltongue while she was possessed by Tom Riddle's Diary, which enabled her to open the Chamber of Secrets.
The Peverells, Gaunts, Blacks, Malfoys, Potters, Weasleys, Prewetts, and other families are all linked to one another through bloodlines and intermarriage. The only known direct descendants from Salazar Slytherin were the Gaunts, who for the most part shared their ancestor's beliefs in the purity of wizard blood.
Their names were Godric Gryffindor, Rowena Ravenclaw, Helga Hufflepuff and Salazar Slytherin.
She is perceptive
Ravenclaws are perceptive, and Luna noticed all kinds of things others didn't during her time at Hogwarts. There was that time she explained Ron in one sentence: 'He says very funny things sometimes, doesn't he?
Slytherin disliked taking students from Muggle families, seeing them as untrustworthy and unworthy of being taught magic, and tried to persuade the other founders to only take students from pure-blood families. However, the other founders didn't agree with Slytherin, particularly Godric Gryffindor.
One of the main reasons Dumbledore belongs in Gryffindor and not Slytherin is because he is willing to sacrifice himself for others. Dumbledore fatally injured himself hunting down Horcruxes and even this did not deter him from his fight against Voldemort.
Harry Potter named his son after the character Professor Severus Snape in tribute to him dying for “for Harry out of love for Lily [Potter],”JK Rowling revealed on Friday.
Peter Pettigrew represents the worst Gryffindor in the entire Harry Potter series. Wormtail, as he was known among his friends, was thought to be a friend of the Marauders and a member of the Order of the Phoenix, but he was secretly working for Voldemort and committed the ultimate act of betrayal in the series.
Godrick Gryffindor, one of the four founders of Hogwarts, and the owner of the legendary Sword of Gryffindor, was absolutely more powerful than Dumbledore— and it's a good thing he was, too, because Dumbledore wasn't around in Hogwarts' early days to keep Godrick's fellow founder Salazar Slytherin in check.
Ginerva “Ginny” Weasley, the youngest and only girl of the seven children, truly did belong in the house of Gryffindor. Ginny's fierce personality, both on and off the quidditch pitch, highlights the courageousness that resides in her heart.