I finally found a page listing relatively current (1998) name registration date for Hungary. (
http://www.registrationshu.org/fuzet/noin1.htm for females
http://www.registrationshu.org/fuzet/ferfin1.htm for males)
According to this list, 20,000+ girls were registered that year alone with the name Enikő, (so it's more popular than I had previously even imagined,) and another 49,000+ with Anikó. Now, if I could only learn the meaning! ;)