Undulopsychopsis alexi is known only from one fossil, the part and counterpart holotype, specimen number CYNB044, which is housed in the collections of the Chaoyang Bird Fossil National Geopark Chaoyang, Liaoning, China.
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The genus name Undulopsychopsis was coined by the researchers as a combination of the silky lacewing type genus Psychopsis and the Late Latin word undula meaning "small wave" which is in reference to the distinctly wavy nature of the wing margins.