Im descended from Joseph Williams and Elizabeth Altree of Shropshire, married at Wolverhampton in Mar 1816. In my case - via their 2nd son Thomas Williams (1825-1909). In our family the middle name 'Altree' was very consistantly used all the way down the generations even to my father who had it as his middle name. It occured in both male and females in this family although it never become a two-barrelled surname as it did with Thomas' older brother - William (1822-1869) line. Our family had lost the specific reason for using the Altree name, only that it was something significant. I've yet to find the reason of the significance of the Altree name to the descendants of Joseph and Elizabeth. Elizabeth did have a 2 x great uncle John Turnpenny-Altree (1736-1798) who sailed as assistant surgeon with the first fleet to NSW in 1787 but this seems an unlikely reason as he wasn't exactly a great success in that endeavor
I did a lot of work on the Altree Williams tree some years ago on familysearch. It appears that it was the children of William Altree Williams (1874-1961) who made it a two-barrelled surname. William b.1874 was certainly the son of William A Williams and Susannah Leicester as confirmed in the 1961 death index [WILLIAMS, WILLIAM ALTREE 18119/1961 WILLIAM, SUZANNA, SYDNEY]. He had moved to Sydney Aus by 1915 with his wife Margaret Jane (nee Smith) 1880-1958 and eight children, adding another two sons - Leslie & George in 1916 & 1918. The first child born in Lancashire was Selina Green (1900-1971) next was Charles Edgar Altree-Williams (1902–1973) who died at Wollongong. [ALTREE-WILLIAMS, CHARLES EDGAR 71283/1973 WILLIAM, MARGARET JANE, WOLLONGONG] .