...the misunderstanding arises from the Greek *ainos* (n) or *aino* (v) meaning "praise".
Classical Greek femaile names related to *ainos* include
Aina, Ainesikrate, Ainesis, Ainesiphile, Ainesio, Aineta, Ainis, Ainete, Ainesa,
Aino, Aineppa, but, alas, no Ainara :)