The composer was Johann Sebastian Bach(1685-1750).
All of them. This is not a trick answer. Johann Sebastian Bach is the most famous of that name, but his ancestors and he and his sons all wrote music for flutes.
In several of his compositions Bach employed a kind of musical signature, his name expressed in musical notes. B signified B flat, A = A, C = C, and H was a German designation for B, so the letters of his name formed the sequence B flat-A-C-B. This is not a typical melody, but Bach used it as a cell on which to build fugues and other contrapuntal structures. Franz Liszt also wrote a fantasy and fugue on B-A-C-H for solo organ.
Bach was organist and master of the choir at a number of different churches in his career, but his last position was the one he held longest - at St. Thomas church in Leipzig.
Christina Bach's birth name is Christina Maria Bach.
Huxi Bach's birth name is Christian Bkgaard Bach.
Robin Bach's birth name is Robin Francis Bach.
Sher Bach's birth name is Sheryl Ann Bach.
William Bach's birth name is William Alfred Bach.
Coming from a family of church musicians and serving as one almost all his life, everywhere he lived: Eisenach, Ohrdruf, Lüneburg, Arnstadt, Mühlhausen, Weimar, Köthen, and Leipzig, as well as every place he visited on sundays, for example on the occasion of inaugurating a new organ. Bach was a Lutheran.
Many composers wrote pieces with "Passacaglia" in the title ... Pachelbel, Buxtehude, Bach to name a few.
Henrik Bach's birth name is Elon Henrik Andrew Bach.