I will defer to more experienced engravers but I'm no "piker" myself having been hand-engraving in the 18th/19th century style for the reenacting set for decades. I started to look at this signature from a cut-by-cut perspective and matching that up with likely letters and no matter how hard I try I can't discern David Duck...
First word - first letter is highly stylized and could indeed be a "D" but it could also be something else - a "J" or an "I" for example. Second letter - definitely a lower-case "a". Third letter has cuts consistent with a lower-case "u" (assuming both cuts are for the same letter) and the last cut...possibly a lower-case "t".
Second word, first letter - almost certainly the same as the first word - a stylized J, I, or part of D. After that I see possibly the traces of a lower-case "r", then something like a lower-case ', c, e, d, or r, etc (all containing similar downward cuts). Fortunately, that last letter is clearly a lower-case "k". Granted, the engraver may very well have had his own techniques and styles but being more than a little familiar with those techniques and styles myself, no matter how hard I try I'm not getting David Duck or "Tuck".
Lastly, I would think if the engraver went to the trouble of adding what appears to have been a nicely done signature, his spacing was not all that great and he left a lot of blank space on the right...after the "k". Hence - another possibility; the lower-case k was somewhere in the middle of the last name.
There are many possibilities and I'd like to hear others from the engraver's perspective.