Possible 1901 for James Dixon -
Barbara Easton   Head M 24 b. Berwick upon Tweed
George Easton   son 1 b. Berwick upon Tweed
Margaret Dixon   sister S 16 b. Berwick upon Tweed
James Dixon   brother S 20 b. Berwick upon Tweed. General Carter
Samuel Dixon   brother S 15 b. Berwick upon Tweed
RG13 Piece 4844 Folio 102 Page 5. 
24 Walkergate LaneThere is a marriage of Barbara Dickson (as transcribed) q3 1898, Berwick, Vol 10b  Page 739. On the same page is George Henry Heston.
Birth of the above George - 
George Henry 
Hestonq3 1899, Berwick, Northumberland
Vol 10b Page 492
Looking at James' siblings from the above 1901 census this may be James on the 1891 with the name Dukson  

 However the name Dukson sounds similar to Dixon-
John F Dukson   head 35 b. Scotland. Rolleyman
Phillis Dukson   wife 33 b. Berwick upon Tweed
James Dukson   son 10 b. Berwick upon Tweed
John Dukson   son 8 b. Berwick upon Tweed
Margaret Dukson   dau 6 b. Berwick upon Tweed
Samuel Dukson   son 4 b. Berwick upon Tweed
RG12 Piece 4267 Folio 90 Page 1. 14 Marygate, Berwick
I have not found the above Dixon family on the 1881 but there is a Forrest Family whose christian names match, birthplaces match -
John Forrest   head 29 b. Scotland. Railway Carter
Phillis Forrest   wife 26 b. Berwick Upon Tweed
Barbara Forrest   dau 6 b. Berwick Upon Tweed
James Forrest    son 12m? b. Berwick Upon Tweed
RG11 Piece 5129 Folio 133 Page 9. 42 Church Street, Berwick.
Baptism for James Forrest -
James Cowe Forrest
Christening Date - 14 Mar 1880, Berwick upon Tweed, Northumberland
Father's Name - John Forrest
Mother's Name - Phillis
Baptism for Barbara-
Barbara Hume Forest
Christening Date - 27 Nov 1874, Berwick upon Tweed, Northumberland
Father's Name - John Forest
Mother's Name - Phillis Rupell
Samuel Dickson Forrest (possibly Samuel from the above 1891, 1901)
Birth Date - 19 Jul 1886
Christening Date - 8 Aug 1886, Berwick upon Tweed, Northumberland
Father's Name - John Forrest
Mother's Name - Phillis
Birth record for Margaret -
Margaret Dickmon Forrest
q1 1884, Berwick. Vol 10 b Page 406
There is another child Agnes 
Dixon Forest, who may have died at the age of two. -
Agnes 
Dixon Forest
Birth Date:   23 Jul 1876
Christening Date - 3 Sep 1876, Berwick upon Tweed
Father's Name - John Forest
Mother's Name - Phillis
Therefore i suggest that James was originally born Forrest/Forest but his parents decided to 'adopt' the name Dixon.
All of this gives 'food for thought' I do appreciate you have yet to establish the correct James, however all the above information may be of help to you in the future  

JJ