There are many different spellings of Asuka's name. This is the correct one from the AD Vision English translation for their dubs.

There are a lot of different spellings of the names, a Japanese way of putting it would be Souryuu/Soryu Asuka Langley. She is 50% American, 25% German and 25% Japanese so that makes the names a bit confusing. Her mother Kyoko Zepplin Sohryu or Souryuu Kyouko Zeppelin was probably 50% Japanese and 50% German so her father was American.

Update 19/04/01

The Second Children, and dedicated pilot of Eva-02. She is one quarter German and Japanese, but her nationality is American. Highly intelligent, she graduated from university at the age of 14 and boasted a higher synchronization rate than the Third Children in the early stages of actual combat. The suicide of her mother led her to develop an overly-aggressive character, and she maintained her mental balance by outwardly publicizing her superiority. Birthdate: December 4, 2001, Blood type: O, Age: 14.

Source: The End of Evangelion : Glossary contained within The End of Evangelion - Theatrical Program.