Eucommia bark is one of the classical 上品 ('superior grade') herbs in 《神农本草经》 (Shénnóng Běncǎo Jīng), the foundational TCM materia medica. Its cut bark uniquely shows fine white latex strands — the source of the 'rubber tree' nickname.
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The name is purely a botanical/medicinal label — 杜 and 仲 are both common surnames, but here they are just phonetic. Don't try to read meaning into the characters.
