Assuming that Hugh B Hossack isn't Buckham Hugh Hossack under a pseudonym, there is no obvious candidate in the Scottish birth and death records.
However there is a Hugh Charles Bu* Hossack who married Lizzie B Low in Newhills (just west of Aberdeen) in 1888.
Hugh Charles Buckham Hossack was born in London in 1861, son of Robert Hossack and Elizabeth Taylor. In 1891 he is in Colwick, Nottinghamshire with wife Bessie, 25 and daughter Maggie H, 4, both born in Scotland, and described as a lithographic artist. He died in 1923, aged 62, and is buried in Colwick.
In the 1871 census in Edinburgh is Jessie Taylor, widow, 73, born England, with daughters Charlotte, 35, and Wilhelmina, 29, and Hossack grandchildren Robert, 17; William, 13; Hugh, 10; Jemima, 7; and Campbell, 5, plus niece Maria Ingram, 25 and nephew George Davidson 15. All born in Scotland except William and Hugh, who were born in England. The niece and nephew were both born in Orkney. Robert Hossack and Elizabeth Taylor were married in Edinburgh in 1852.
Jessie Davidson or Taylor, 79, died in Edinburgh in 1878, mother's maiden surname Buchanan. Could Buckham have been a misinterpretation of Buchanan, or vice versa?
I can't guarantee that Hugh Charles Buckham Hossack is the Hugh B Hossack who painted your painting, but if he was, then it does look as if there is a connection. More research needed!
