Arya Stark: A skilled fighter who would swear her Kingsguard vows before a statue of the Many-Faced God
The first and easiest pick for Jon would be his little sister-cousin Arya. In a way, appointing her to his Kingsguard would complete a story that started in season 1, when Jon had the Winterfell blacksmith forge a sword for her as a gift. Arya named the sword Needle, bloodied it up a lot over the following seasons, and still fights with it to this day. It’s long represented her connection to her family, and being on Jon’s Kingsguard would mean she could always put it to good use. And her Valyrian steel dagger could come in handy, as well.
During her long journey, Arya learned how to fight like a Braavosi Water Dancer from Syrio Forel, like a rough-and-tumble brawler from the Hound, and like a deadly assassin from Jaqen H’ghar of the Faceless Men. Having had so much training in so many different disciplines, Arya is more than capable of holding her own as a member of Jon’s or anyone else’s Kingsguard. She proved that when she fought the incredibly capable Brienne of Tarth to a standstill after returning to Winterfell in season 7, despite Brienne having a considerable height and reach advantage on her.
When the war against the Night King is won, Arya won’t be content hanging around Winterfell, but if offered the opportunity to become a member of her brother’s Kingsguard, she’d likely accept on the spot.