1) The study of personal names 
Anthroponomastics (or anthroponymy), a branch of onomastics, is the study of anthroponyms (
(from the article `name`) ...names of persons, or personal names, are discerned on the one hand, and names of places, or place-names, on the other. In the most precise ...
anthroponymy Personal names as a subject of study or the study of personal names.
the study of personal names.