How to write a string in eeprom ?

mem is right-- the EEPROM_writeAnything() has to have a known size. An EEPROM_WriteString() derivative would not be hard, if you think about how strings are addressed.

The problem then becomes how to read it? Do you want to read it back into a fixed buffer of a known size? (If so, you probably should have written from a fixed buffer as well with the aforementioned function.) If you just want to read it character by character, then EEPROM_read() is fine.