Du Mu and Du Fu are not related by blood.
Du Fu (a famous realistic poet in the Tang Dynasty): (7 12 -770), Zi Meiren, Han nationality, Xiangyang native, moved to Gong County, Henan Province. A great realistic poet in the Tang Dynasty, who claimed to be a young man at night, was called "Du Li" together with Li Bai.
Du Mu (803- 852) was born in Fanchuan, Mu Zhi, Han nationality, Jingzhao Wannian (now Xi, Shaanxi). Because he lived in South Fan Chuan Villa in Chang 'an in his later years, he was later called "Du Fanchuan" and wrote "Collected Works of Fan Chuan".
Du Mu's poems are famous for their seven-character quatrains. Du Mu is called Xiao Du, which is different from Du Fu and Da Du. Also known as "Little Du Li" with Li Shangyin.