Singer or happy
As a Persian name, it is a variant of Shadi, meaning happiness or joy. In an Arabic context, it is a variant of Shadi, referring to a singer or someone who recites. It is occasionally used in English-speaking contexts as a modern nature-inspired name relating to shade.
Less common today
Shadee isn't in the latest US Top 1000. It last peaked at #7,858 in 1993.
US births per 5-year period, 1990βpresent (SSA data).