Berwick Holy Trinity:
Alexander Crossman baptised 23 oct 1842 s/o Robert and Sarah Crossman, Brewer of Quay Walls, Berwick
Eliza Crossman baptised 20 Mar 1845 d/o Robert and Sarah Crossman, Brewer of Silver St. Berwick
Alexander Crossman baptised 26 Jan 1846 s/o William and Mary Crossman, Attorney-at-Law of High St. Berwick
Sarah Marshall Crossman baptised 11 Oct 1849 d/o William and Mary Crossman, solicitor of Bridge St. Berwick
Just some more Crossman's for your list--also of note there was a Thomas and Margaret Gilchrist and Thomas was an attorney-at-law also.
There was also a Gilchrist family in Berwick that were brewers having children in the 1850's--William Nesbitt and Eleanor Gilchrist
If Alexander seems like a likely name there was a baptism in Spittal Presby of a Alexander Gilchrist 27 Mar 1868, born 24 Mar 1868 s/o Alexander and Elisabeth Gilchrist. There was also a Rachel Gilchrist born 1765, same parents
There was a family having children in the Berwick area with the parents Alexander, grocer, and wife Eleanor, these were in the 1820-1830's. (Bapt Berwick High Meeting House)
Also a Captain William Crossman, Ship Captain, and wife Jane Cameron
Janis