but the lastname Decker is of sure german!
and Rosina is definitly not "only italian",it´s of latin orgin and also since 16th century usual in Germany, specially in Würrtemberg and Sachsen. after end of 19th century it was not longer a ususal name in Germany.
so in fact the name Anna Rosina Decker looks sounds very german.
"Allerdings war er bereits ab dem 16. Jahrhundert in Deutschland, insbesondere in Württemberg und Sachsen, stark verbreitet."
http://de.wikipedia.org/wiki/Rosina