Let's break it down
MarieClaire.com breaks the royals name into three examples.
Exhibit A: "You-Jenny"
Exhibit B: “You-Jay-Knee"
Exhibit C: “You-Genie” (like "Genie in a Bottle")
However, it turns out that none of these are actually correct.
According to a 2008 Telegraph interview with the princess herself, it's actually pronounced “You-Juh-Knee" with a stress on the "you."
"Whenever we used to meet foreign people who were struggling with it, my mum and I would help them by saying, 'It's like Use Your Knees,'" she says.
"But whatever. I am now used to every pronunciation."