It is implied that the extent of the power and authority granted Saul was limited to the Jewish people at this point in time. (see: [[rc://en/ta/man/translate/figs-explicit]])
"Chosen instrument" is an expression for being set apart for service. It can be translated as "I have chosen him to serve me." (See: [[rc://en/ta/man/translate/figs-metonymy]])
"to carry my name" is an expression for identifying or speaking out for Jesus. It can be translated as "in order that he might speak about me." (UDB) (See: [[rc://en/ta/man/translate/figs-metonymy]])