// instead of  String  you can use  char*
#include <LiquidCrystal.h>
LiquidCrystal lcd(12,11,10,9,8,7);
//String ch_imena[3]={"Janez", "Mojca", "Angelica"}; //seznam tipa String
char ch_imena[3][11]={  //seznam tipa char
  "Janez",
  "Mojca",
  "Angelica"
}; 

void setup() {
  lcd.begin(16,2);
}

void loop() {
  for(int x = 0; x < 3; x++){
    lcd.clear();
    char *m = ch_imena[x];
    //String m = ch_imena[x];
    tekstPrint(m, x);
    delay(500);
  }
}

void tekstPrint(char *tekst, int y){
//void tekstPrint(String tekst){
  lcd.setCursor(0,0);
  lcd.print(tekst);
  lcd.setCursor(0,1);
  lcd.print(y);
}