They might have written the part for a "Sulu-like" Oriental, but then cast Tony Shaloub and just decided to keep the name.
That's great explanation for both the actual movie and the in-universe show.
So many stories, so little time.

They might have written the part for a "Sulu-like" Oriental, but then cast Tony Shaloub and just decided to keep the name.

I hadn't noticed this but it sounds funny. I'll have to watch for that.

It's a running joke in the movie that the Tony Shalhoub character is a non-Asian man cast as a Chinese man. I think that toward the beginning, he's trying to squint all the time.
I wonder if this joke was in the film even before Tony Shalhoub was cast. It's a running joke with HIM that he's been cast as many different ethnicities, and then done whatever accent was called for. Italian, Pakistani, maybe Latino, European American, Indian, Middle Eastern. As I recall.

You don't have to look Asian to be an Asian..
With all the race mixing these days it's hard to know for sure if someone's last name is false or for real..
"
Gar nicht so bel, du kleine Schlampe. Man sieht sich immer zweimal, Kleine.
"