There's plenty still unknown about Neil in Tenet - could he be the son of Sator and Kat? In the spy game, mystery comes with the job description, but Tenet's Neil takes enigmatic espionage to an entirely new level, not only concealing his identity and intentions, but even the era from whence he came. At some point in Tenet's bleak, unseen future, Neil is recruited into the Tenet organization by John David Washington's Protagonist. By use of a turnstile, Neil's entropy is inverted, sending him backward to Tenet's present where he meets a younger version of The Protagonist, and sacrifices himself to save the world from Sator.
Along the way, Neil and The Protagonist team up with Kat, Sator's deeply unhappy lover. Although the couple have a son together, Kat has become disillusioned with her controlled existence, but Sator blackmails her into staying by his side. In assisting The Protagonist, Kat is finally able to break herself and her son, Max, free from Sator's clutches. While Tenet draws no explicit connection between Neil and Kat, one of the film's most popular fan theories suggests Neil is actually a grown-up Max.
Tenet makes frequent use of palindromes to accentuate the film's presiding theme of inversion, and this is true even with character names - Sator's company being called Rotas, for example. If we assume the full name of Sator and Kat's son is actually Maximilien, inverting the word gives "Neil." With all due respect to the Neils of the world, it's not the first name you'd pick for a suave spy character, but being an invert of Maximilien might explain why Nolan chose it. Additionally, Tenet's ending reveals how The Protagonist continues watching over Kat and Max after the film's events. When the boy becomes an adult, The Protagonist could keep Max close by recruiting him into Tenet (especially after noticing his increasing resemblance to Robert Pattinson). Also, the connection to Sator would explain why Neil is willing to give his life to stop the Algorithm - the son paying for the sins of the father.
Neil's British upper-class background matches Kat's, and as Reddit user yeetabix35 points out, Pattinson's character asks The Protagonist whether he'd take a mother and child hostage, alluding to Sator's treatment of Kat and Max. The same Reddit post also believes the coin on a string that identifies Neil's backpack could be a souvenir from Vietnam, where Sator took his family on a fateful vacation, and Kat finally earned her freedom.
Predictably, the "Neil is Max" theory isn't without flaw. Neil shows very no emotional response to seeing a younger version of Kat, and even acts annoyed when The Protagonist prioritizes her safety above the mission, implying she isn't his mother. And given the age gap between Max and Neil (20 years, at least), the latter would've had to spend years inverting in order to double-back so far into his personal timeline. One could also argue that Kat would hate for her son to become a spy in adult life, and The Protagonist wouldn't have betrayed her wishes by knowingly bringing Max into Tenet.
With that said, Neil's Tenet history is so vague, the possibility of him being a grown-up Max is entirely plausible - and would actually improve the film if true. Neil and Max being the same person gives a more meaningful explanation as to why The Protagonist recruits him in the future, and provides Neil with a more emotive motivation for opposing Sator. The connection compliments Christopher Nolan's overall theme of inversion, and adds personal stakes to a story that often prioritizes plot over character.