The origin of the Hungarian name
Anikó
has the following meaning:
Favor; grace.
The etymology of "Anikó"
is 
Hungarian pet name for Anna.
This meaning also applies to these versions: Aniko
Other information:
 
 
Etymology is the study of the origin of words, and in this case, the origin of names. 
The word etymology comes from Greek 
etymon, "true sense of a word", and logia, "doctrine or study".