It's possible that the coat was:
* Custom-made for the film, as many costumes are for Hollywood productions.
* From a high-end designer not specifically mentioned, like Tom Ford or Ralph Lauren.
* From a lesser-known brand chosen for its look and fit.
If you're keen on finding a similar coat, you can try looking at similar styles from brands like Barbour, Belstaff, or even Zara.
Ultimately, the exact brand remains a bit of a mystery, adding to the mystique of Tom Cruise's character in the movie!