There has been much debate about the correct pronunciation of Roosevelt's last name, however, in several letters Theodore Roosevelt himself specifies the correct pronunciation. In a letter to the Rev. William W. Moir dated October 10, 1898 he writes:

As for my name, it is pronounced as if it was spelled "Rosavelt." That is in three syllables. The first syllable as if it was "Rose."

Source: Theodore Roosevelt Cyclopedia, pages 534-535. Available online at http://www.theodoreroosevelt.org/