From the Adriatic; dark
Adrena is most likely a creative variant of Adriana or Adrienne, names derived from the Roman family name Hadrianus. It refers to a person from the town of Adria in northern Italy, which also gave its name to the Adriatic Sea. In some contexts, it is associated with the Latin word for 'dark' or 'black' due to the dark sands of the region.
Less common today
Adrena isn't in the latest US Top 1000. It last peaked at #7,136 in 1992.
US births per 5-year period, 1990βpresent (SSA data).