OK, just because this search for Robert is so complicated, which at some point makes you wonder whether he may have been illegitimate, and also the names for mother are varying as are Robert's age and his father's occupation, just adding this birth entry from 1870:
https://familysearch.org/pal:/MM9.1.1/XYT4-HMKJane comes up on his death cert in 1918...although no surname
Following on with my theory that Robert may have been registered as Anderson, there is this 1871 census entry:
Peter Anderson 44 general labourer
Ann Anderson 43 b. Edinburgh
Jane Anderson 21 daughter b.
Rob Brown 7 Months grandson b. Aberdeen
Margaret Anderson 13
https://familysearch.org/pal:/MM9.1.1/XYR4-3YVMary Anderson 7
https://familysearch.org/pal:/MM9.1.1/XYRW-5VFAgnes Anderson 5
https://familysearch.org/pal:/MM9.1.1/XYR4-673Address: 7 Peacocks Close, Aberdeen St Nicholas
Maybe this is the source of the name Peter born in 1901 to Robert and Margaret (Peter Anderson)?
Monica
Added: All fine and good as a possibily, but cannot jump from here to the surname Thomson so far...
Also, there is this entry for 1881, still closer to Brown than Thomson:
Jane Anderson 28 millworker
Maggie Anderson 23 millworker
Mary Anderson 18 millworker
Robert Brown 10...son of Jane
Address: 6 Murrays Court 24 L St West, Aberdeen