I've got a James Anderson, who was apparently born in 1846 or 1847 in Bath, but I can't find any possible birth registration, nor any likely record of him before 1881.
The first I have of him is from the 1881 Census for Sunderland. He's listed as living at 45 Hendon Street in Sunderland, birth year estimated 'about 1850' (Ancestry), and apparently married to Mary Ann Anderson (b. 1847).
The couple had at least 2 children, Edward (b. December 1879), Alfred (b. May 1883). Both born in Sunderland. Mary Ann's maiden name was BAILEY.
A third child James Anderson is also listed, 5 years old, in 1881. I can't find a birth record for him either, and he seems to be limited to that census.
Mary Ann, by the way, was married to an Edward COE from Essex (who died in 1873), he fathered at least 3 children to her, Isabella Ann (b. 1864), Mary Ann (b. 1867) and Georgeine (b. 1872). They are listed as step children of James in 1881.
James appears once again in the 1891 census, 'aged 44', husband of Mary Ann, and the father of Edward and Alford (sic). No other occupants. James is recorded as having died in 1895.
I have no reason to suspect James Anderson ever used any other name, but that's a possibility worth not losing sight of entirely.
