McMurray was not a common name here in Motherwell, there were only 4 McMurray households listed in the 1911 street directory for the town. The householders names were :-
McMURRAY Henry, ironworker, 98 Wellington Street.
McMURRAY James, plater, Thistle Street.
McMURRAY Mrs Mary Ann, Kilmoray, Douglas Street.
McMURRAY Mrs Mary, 32b North Orchard Street.
In the 1922 street directory (compiled as a voter's roll rather than a list of head of households)
McMURRAY B. 36 Ashton Place, Airbles Street.
McMURRAY C. 11 Forrest Street.
McMURRAY J. 11 Forrest Street.
McMURRAY R.F. 117 Brandon Street.
In the 1925 Householders list (compiled by streets) all of the above are still at the same addresses,
McMURRAY BERNARD, miner, 36 Ashton Place, Airbles Street.
McMURRAY C. fitter & McMURRAY JOHN, steelworker, 11 Forrest Street.
McMURRAY ROBERT, draughtsman, 117 Brandon Street. (That address is still there, a tenement).
There was a family of McMurrays lived in Kings Building, Merry Street when I was young (2 years ago!

) I just rang one of the daughters who still lives in Motherwell, she said her father's family originally came from Ayrshire and he only came to Motherwell for work in the 1930's.
Hope this helps.