Traditional Chinese medicine often uses eucommia to tonify the kidneys and strengthen the lower back.
Tips
culture
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.
memory
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.