Three possible explanations it seems - 1.From the dialect word yesenia, meaning Autumn, osen' in standard Russian. In this case it is taken to be a name or nickname for a child born in Autumn. 2. A diminutive form of the male given name Evsevii (Greek Eusebius) 3. A diminutive form of the male given name Yesip a variant of Yosip or Yosif (Joseph).