People seriously see the 3DS as another separate line from the DS like DS was to GBA?
Well it depends on how you think about it. If you believed Nintendo back when they said they were supporting the GameBoy, GameCube, and DS brands as separate entities I guess the same could be thought of for the Wii, DS, and 3DS brands. But that was just so they could sell the remaining GBA hardware and get away with releasing the GB Micro. The GameBoy brand died when Pokemon Diamond and Pearl were announced.
If you really think about it(which shouldn't take much effort, like, at all), Nintendo's handheld console line has held a completely linear path from the original GB to the 3DS. The 3DS is to DSi as the DS is to GBA SP (and GBA to GBC and so forth)
The name isn't anything other than mixing 3D and DS using the same D from both. The hardware itself and marketing through in-store demos and word of mouth from people like us from the Internet will let the general public realize that this is more than just a small upgrade like the DSi or GBA SP.