With regards to Deed Polls now, you can complete a deed poll to legally change your name but there is no requirement to lodge this anywhere, so you can legally change your name without any official record being retained. Whether that was the case back then I don't know.
There is currently a programme in BBC called Turn Back Time The Family. One of the families, the Goldings were Jewish and on the second episode there was a short segemnt about the fact that they changed their name in the 1920's. I can't remember well enough but they might have mentioned where the document was from. The episode is still on iplayer if it might help.
