What are names of fake diamonds?

You can ask for CZs, crystals, glass, ice and find what you're looking for. Moissanite can also pass very successfully for diamond.

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Keep in mind that De Beers would like man-made diamonds classified as "fake" but they are definitely REAL. Man-made diamonds have the exact same chemical composition and structure as those dug out of the ground. Gem-quality diamonds grown in a lab can be chemically, physically and optically identical (and sometimes superior) to naturally occurring ones.