Looking at the two images it seems to be clearly Deddy-something or possibly D'Eddy-something
There is a lady and 2 year old daughter with a similar name in the 1901 census at 23 St Andrews Mansions, St Marylebone. Looks like Mrs Deddyln, 22, and daughter Kathleen, 2, both from Brickley (?Bruckley?), Scotland.