The Game of Thrones series has far surpassed the books that it is based on, meaning that some characters' ultimate GoT fate won't be the same fate they meet in A Song Of Ice And Fire. However, given what happens to Arya in the books, it's entirely possible that Arya's book ending could line up with the show ending, but it's also possible that readers of ASOIAF will be following Arya as she goes down a path that will diverge slightly from the show, or a path that could take Arya in a vastly different direction from what fans of the show could expect.
Arya Stark has proven herself to be the hero of Winterfell in the final season of GoT, but she's still got a long way to go in the books if she's going to bring an end to the Night King. At the end of A Dance Of Dragons, Arya is in the exact spot she's in at the beginning of Season 6, training with the Faceless Man to become "no one." In the show, Arya is tasked to spy on theater troupe from afar to kill the actress Lady Crane, but an early released chapter from Winds of Winter reveals that Arya actually becomes an actress herself in the company under the name of Mercy.
This marks an interesting direction in Arya's training in the books that the show doesn't go into much — not just how Arya can look like other people, but how she can act like them as well. Arya's theater course seems suited for such a purpose. The books haven't introduced Lady Crane, so it's possible that she may not even appear in the books and that Arya's falling out with the Faceless Men comes about another way, if at all.
While in the show Arya manages to make her way back to Westeros to put an end to the Frey household and eventually become to person to strike down the Night King, the books may find her on a different path and could even see her following through on her training and becoming no one. Arya Stark renouncing her name and becoming "no one" would mark a huge change from the shows, but that name won't go to waste because someone else in the books has already it.
In the books, many characters believe that Arya Stark is alive and is being wed to Ramsey Bolton. In the books, Ramsey's bride-to-be and object of his cruelty is not Sansa Stark, but is instead her childhood best friend Jeyne Poole that is believed to be Arya Stark. The only person associated with Ramsey who knows that Jeyne isn't Arya is his servant and slave, Theon Greyjoy. Jeyne has been keeping the lie that she is Arya up because if anyone knew that Jeyne Poole wasn't actually a Stark, there would be no reason from the Boltons to keep her alive.
Jeyne manages to escape Bolton's hold with the help of Theon Greyjoy, just as he helps Sansa in the books, which is where fans leave fake Arya in A Dance With Dragons.
With two Arya Starks roaming The Realm, there's bound to be a difference in how these stories end up in the books. While Arya has persevered time and time again after many hardships in GoT, one or both of the Aryas in ASOIAF have a long way to go before they reach anything close to safety.