Evelyn's history is layered, moving from a Norman surname into a given name, and it's often associated with the idea of a long-desired or wished-for child. That association gives the name a gentle, hopeful undertone -- less about destiny and more about being welcomed. Its meaning has shifted across centuries of use.
Understand the simple qualities of the Planets, for from thence thou shalt know all their mixt significations. - William Lilly (1602.-1681.)