The sources checked do not record Batzi as a personal name or give it a meaning.
Playful
Cute
Gold, Black, Brown, White
Small
Unisex
Others
B
5 Letters
A Kashubian feminine given name
A diminutive of Andrés
A feminine given name recorded in modern English
A surname
Polish diminutive of Barbara; also a Hebrew diminutive of Batyah.