With Hebrew Origins, Anica Is A Charming Girl’s Name Meaning “favored Grace.” Though Not As Popular In The United States, Anica Is The Slavic Diminutive Of Anna. More Popular In Slovenia, Croatia, And Serbia, Anica Is Pronounced, “ah-nee-tsa.” There Have Been Several Well-known Anica’s From Eastern Europe Including Slovene Author And Poet Anica ?ernej, As Well As Writer Anica Boškovi?. If You’re Looking To Be Inspired By Your Eastern European Roots, Anica Is A Great Fit.