Going back to Recke, although it could be very interesting, would still not provide the proof you need. I would say the two names refer to the same person and it would seem reasonable that he would change his names to fit in with the English speaking country he had settled in but it would be there that the proof would lie. Even if you found the arrival record it would only be under one form of the name, probably the German one and you would still not know if the Anglicised form found later was the same person. Perhaps a marriage certificate would record the German form and then it could be traced to see if a resident with the anglicised version was living with a wife of the "marriage" name? What about a child's baptism record? The father could well have been using the German form in his church but a later, residential, occupational record would prove that the child was living with a father with the Anglicised form. Bit of lateral thinking needed!