the 'Goldsource' engine, and the name stuck. When it came down to show Half-Life 2 for the first time at E3, it was part of our internal communication to refer to the 'Source' engine vs. At least initially, the Goldsrc branch of code referred to the codebase that was currently released, and Src referred to the next set of more risky technology that we were working on. Over the next few years, we used these terms internally as 'Goldsource' and 'Source'.
At that point we forked off the code in VSS to be both /$Goldsrc and /$Src. When we were getting very close to releasing Half-Life (less than a week or so), we found there were already some projects that we needed to start working on, but we couldn't risk checking in code to the shipping version of the game. Valve employee Erik Johnson explained the engine's nomenclature on the Valve Developer Community: Carmack commented on his blog in 2004 that 'there are still bits of early Quake code in Half-Life 2'.
Source distantly originates from the GoldSrc engine, itself a heavily modified version of John Carmack's Quake engine with some code from the Quake II engine.