as raulpica and others have said, there is no such thing as a fake DS. though the screens and shell might be reproduced on the cheap, the actual hardware and software (motherboard, processor, ram, firmware) will all be official nintendo stuff.
reverse engineering hardware like that, and reproducing it unofficially would be an accomplishment of astronomically impossible magnitude. it took 10 years for china to reverse engineer the GBA hardware, and package it into a semi-working knock off - a machine vastly less complex than the DS is. it's simply an impossibility that they've managed to do the same with a DS.
so yes, maybe your LCDs and casing are not legit, but if it boots to the DS firmware and plays DS carts then the innards will be of a real DS without any doubt.