He did indeed face a kind of "no-win situation" - Japanese intelligence learned that the US planned a major attack on the Truk naval base (read: the US planned to completely destroy the Truk naval base.)
Vice Admiral Masami Kobayashi ordered that all naval assets be moved from Truk to other bases, knowing that there was not time to move all ships and personnel and that there was no time to mount a workable defense - Truk and most of its ships and personnel were doomed no matter what action he took. The Truk naval base was indeed destroyed, and most of its ships and materielle was sunk in the lagoon.
That sounds like the basis of the Kobayashi Maru test in the Star Trek series - you are sunk no matter what you do.
I searched a bit (this site and the internet in general) but I didn't find anything that indicated that the authors who devised the "Kobayashi Maru" test knew of Vice Admiral Masami Kobayashi. Most of what I turned up indicated that the origin of the ship's name "Kobayashi Maru" is unknown - mostly just speculation that "Kobayashi" is a made up word, though as it turns out it is indeed a normal Japanese name (I have since found other people with that name.)
Has anyone ever seen or read anything where one of the authors of "The Wrath of Khan" explains the "Kobayashi Maru" test, and maybe explains how the name was chosen?
Background (skip if you like.)
The Truk Lagoon is a somewhat famous place for divers - the wrecked ships are not very deep, and therefore accessible to many divers (provided they can make the trip to Truk.) I first read about it in a National Geographic article some time in the 1970s. The article was mostly about diving in the lagoon, and included a lot of photos of the wrecks.
My son reminded me of it this morning. One of his friends has bought a large aquarium, and intends to build a sort of WWII diorama for the fish to live in. The thought of wrecked tanks and trucks underwater reminded me of Truk Lagoon, and here we are.