I actually do know the answer to this question. It is because the initials NGC were already taken by another game system, the Neo-Geo Color. In order to avoid confusion, the next best thing was simply picked as the initials, GC.
As Maxyboy13 said, it's because NG is NeoGeo. The system is NeoGeo Pocket Color, or NGPC, but NG would still be an infringement on NeoGeo, so Nintendo simply wanted to avoid that.
Here's a similar question to the thread starter's question. Why was the original Playstation refered to as the PSX? Not to be confused with the actual PSX, which was released nearly 10 years later.
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