The license plate assembly. What's it called?

License Plate Assembly Name
The part you're referring to is typically called the license plate lamp assembly or license plate light housing. It includes the bracket or frame that holds the plate, plus the lights that illuminate it. If you're replacing it, you might also see it listed as a license plate bracket, license plate frame, or body & lamp assembly – license plate depending on the catalog.

1992 Isuzu Trooper LS: Big Horn or Jackpot?
Your 1992 Isuzu Trooper LS is most likely neither Big Horn nor Jackpot—those names were used for Japanese domestic market (JDM) variants or special editions. In the U.S., the Trooper LS was a higher trim level featuring upgrades like:

• DOHC 3.2L V6 engine with 190 hp
• Optional four-wheel ABS
• More upscale interior and features compared to the base S model

If your Trooper was imported from Japan, it might carry the Big Horn badge, which was a luxury-oriented version. Jackpot, on the other hand, was a rarer, more playful trim name used in some limited JDM runs—not typical for U.S. models.