Noble, well-born, or genius
Geniya is a rare diminutive or variant of the Russian name Evgeniya, which is the Slavic form of Eugenia. It ultimately derives from the Greek name Eugenios, meaning well-born or noble. In some contexts, it is also associated with the word for genius or spirit.
Less common today
Geniya isn't in the latest US Top 1000. It last peaked at #6,691 in 2002.
US births per 5-year period, 1990βpresent (SSA data).