In Rush Hour Jackie Chan's character is called Yan Naing Lee:
Chief Inspector Lee is one of two main protagonists of the Rush Hour series. He is a Chief Inspector with the Hong Kong Police Force (H.K.P.F). Lee appears in all three of the films. He is partnered with Detective James Carter, who at first doesn't get along with, but later befriends. Lee is portrayed by Jackie Chan.
He's often called Lee in the film, so most likely that means his surname is Lee or 李 (can't imagine it'd be anything else).
As for NAING, it seems to be a romanization of a Burmese name - if anything.
Chinese searches bring up names like:
YAN NAING OO陈馨丰
where NAING would, assumably, be 馨, based on allignment. This, though, seems to be made-up Chinese name - rather than a translation or a transliteration - what have you.
The only other thing I can find with Naing (and even Yan together!) is this translation:
博杨莱-德钦通盛(Bo Yan Naing-Tun Shein)
I'm not sure what this romanization system is either. If it was a true translation then that would make the characters name something like: 李杨莱.
Not finding much online - as the Chinese just refers to him as Officer Lee (李警官).
Edit: saw 有道 also lists:
Why would a movie character from HK have Burmese or Cambodian romanization in his name? Bizarre.