I can't find that corresponding 1864 birth on GRO. Maybe some are just missing.
Colonel Stodare definitely goes by Joseph on his death cert:
London, England, Church of England Deaths and Burials, 1813-2003
Joseph Colonel Stodare
died: 22 Oct 1866 • 5 Springfield Terrace, Kentish Town, Middlesex, England
Father: Joseph Stoddart
Mother: Priscilla Woods
Brother John Stoddart's birth in 1841 showing mom's maiden-name:
Name: Mother's Maiden Surname:
STODDART, JOHN WOODS
GRO Reference: 1843 M Quarter in PENRITH UNION Volume 25 Page 136
------------------------------
22 Oct 1866 Joseph Stodare lived at the Egyptian Hall, Piccadilly, Middlesex, England