Enthusiasm or ardor
Rhyse is a modern spelling variant of the traditional Welsh name Rhys. It stems from the Old Welsh word 'ris', which translates to enthusiasm, passion, or impulsive heat. While historically masculine, this spelling is increasingly used in a unisex capacity in the United States.
Less common today
Rhyse isn't in the latest US Top 1000. It last peaked at #4,556 in 2009.
US births per 5-year period, 1990βpresent (SSA data).