Derived from the Georgian adjective ნაზი
(nazi) meaning "gentle" as well as "delicate, soft, tender", which is ultimately derived from the Persian noun ناز
(naz) meaning "coyness, coquetry". This word is not to be confused with the Persian noun ناز
(naz) meaning "pride" (see names like
Golnaz and
Shahnaz). With that said, you might want to compare the name Nazi with the Turkish name
Naz, the Arabic name
Nazli and the Persian name
Sanaz, all of which are probably etymologically related.
A known bearer of this name is the Georgian-American chess player Nazi Paikidze (b. 1993).