i am learning english at the moment

Six hundred years ago, Sir John Hawkwood arrived in Italy with a band of soldiers and settled near Florence. He soon made a name for himself and came to be known to the Italians as Giovanni Acuto.

does [made a name for himself] mean he changed name for himself or it means he become famous in italian

It means he became famous.

Sra

In the given context, "made a name for himself" means that Sir John Hawkwood became famous or well-known. It does not mean that he changed his name. It means that he gained recognition and his reputation grew. In this case, it means that the Italians became aware of his achievements and abilities, and that's why they started calling him Giovanni Acuto. So, to summarize, "made a name for himself" implies becoming famous or gaining a reputation, not changing one's name.