ディエゴ is phonetically closer. Though we do not have appropriate Kanji that matches your name, I would suggest you to use "醍醐" (pronounced "daigo"). This is an elegant name (which means an ancient ambrosia like cheese) and was also used by an emperor of Japan some 1100 years ago.

We write names in japanese with katakana ...So Diego --> Jiego ヂエゴ