Did a search for Robert Smith (the 13 year old brother of the Joseph H. Smith in 1891 in Wales), born Canterbury, in the 1901 census. Only about 20 Roberts in total, who were down as born in Canterbury, two years either side of 1877. No Robert Smith, however, there is a Robert Brown, and he's living in Chester le Street.
1901 census, North Burns, Chester le St., RG13/4699 page 14.
Robert Brown, head, married 23, Core (?) Hewer, b. Canterbury, Kent
Agnes Ann Brown, wife, 22, b. Pelton Fell
James W. Brown, son 7m, b. Chester le Street.
Looking on FreeBMD for an Agnes Ann, b. Chester le Street (Pelton Fell is in Chester le Street district). Only one around the right time is :
Agnes Ann Bankhead, b.Chester le Street, Jun qtr 1878, vol 10a p. 571.
Looking then for a marriage of Agnes Ann Bankhead. On FreeBMD she married either Peter Hanley or Isaac Robert Smith. Chester le Street, Sep qtr 1898, vol 10a page 825. Durham County Council website confirms she married Isaac R. Smith.
Looking for a birth of Isaac Robert Smith on FreeBMD, only 2 on record. One in 1858, and one Dec qtr 1877 in Canterbury, vol 2a p 272.
Looks like they moved north and gradually all took their stepfathers surname.
Welcome to the Smith family.
Alan.