Instead the story is that the source engine was located in the "Src" directory in their Visual Source Safe. And the Half Life 1 engine was in a separate branch named GoldSrc because it was about to ship real soon, and they needed to keep changes to a minimum.
That's not why it's called that. The real reason is that they didn't bother ever giving it a name. When they needed a stable fork so they could further develop the engine without interfering with the development of Half-Life, they referred to the two source codes "GoldSrc" and "Src" and the name stuck.