I'd assume it's short for a long name ending in -ency, sort of like
Enzo for
Lorenzo. I don't like Ency as a full name. I think it reminds me of too many words like emcee, etsy, antsy...
It could also be a "y" nickname for a name ending in -ence.
Some full names...
Clemency Clemence Florence PrudencePatience
Montmorency
Clarence Laurence Terrence
And middle names...
Ency
Dorinda Ency
Petunia Ency
Margaret Ency
Jane Ency
Beatrice Ency Floralinda
Ency
Georgia Ency
Bettina Ency
Jacqueline Ency
Lilibet Ency
Michaela Ency
Abigail
Ency
Charles Ency Donahue
Ency
Willoughby Ency
George Ency
Baldwin Ency
TheodoreEncy
Philip Ency
Augustus Ency
Louis Ency
Sebastian Ency
Michael Ency
Horatio