In Spanish cultures, and spelled either Bastian or Bastien, this is a fairly common nickname name. The German fantasy children's book The Neverending Story features a young boy character called Bastian Balthlazar Bux, and it has also been seen in several screen versions.
Bastian has been enjoying recent popularity in Latin America: it reached Number 11 in Chile--as well as in Germany and Scandinavia, and is just beginning to be appreciated here. Jeremy Sisto used it for his son.
Alternate spelling Bastien is also a fashionable Euro form with a possible future in America. There is a one-act comic opera by Mozart titled Bastien und Bastienne.