Do you know if Duda originated in Poland?
I really do not know that for sure. But consider the fact that the word "duda" exists in several languages. For example "duda" is apparently a Hungarian name for bagpipes, en.wikipedia.org/wiki/Duda
These instruments were associated with shepherds and a pastoral lifestyle. Polish original name for bagpipes was "koza" (from skin of "koza", a goat). The "gajda" name was popular in Balkans, which have been transformed into plural "gajdy" in Polish, Czech and Slovak languages.
I would assume that word "duda" came to Polish language with Wallachian shepherds, exposed to Hungarian name "duda", who started settling in Polish Carpathians at 16th century or so. It might be instructive to take a peek at distribution of "Duda" surnames in Poland - most of them are concentrated in southern Poland: the foothills of Carpathians and Silesia, moikrewni.pl/mapa/kompletny/duda.html.
But this is immaterial now with respect to your family search. Duda surname has been long established in Poland, as it is proven by the sheer number of people using this surname, 36,647.See also, some words about etymology of "duda":
Duda, dudku, dudarz and dudziarz - a bagpipes player.
Dudki, dzidy - animal guts. "Znowu mu dzidy potężnie opiorą" (They will beat his guts massively again), Potocki.
Basic Slavic musical instrument. Serbs and Bulgars used to call it "dud", but now they use the Turkish borrowing "duduk".
Germans, in turn, borrowed the "duda" word from the western Slavs in the words Dudel, Dudelsack, dudeln.
Onomatopoeic, (dudu=mova=> speech) as in "o mszy ani dudu" (not a whit about the Mass), Potocki.
In folk dialects: "odudzieć" = oniemieć (to become dumb)
Dudnieć and dudnić (to rumble) - in description of dull, muffled sound.
Carried into "hollow things", such as pipes:
- dudło, dudłazy => holes in the tree,
- dudlić and dudlać (to pick, to gouge)
Dutki - sad singings
See also "Encyklopedia Staropolska) (in Polish) - Old Polish Encyclopedia
Dudy, musical instrument, known throughout Europe for centuries, also called a goat or Wołynka and improperly pipes. Moraczewski writes that in the eighteenth century it was known only in some areas of Wielkopolska.
Dudy were once in Poland instrument commonly used in all states. The famous conqueror of the Turks, Samuel duke Korecki, taken in the days of King Sigismund III to slavery, being herded on foot to Istanbul, played his dudy to comfort companions of misery and make the exhausting march lighter.
From: Slav music and instruments (in Polish)