To make a name for yourself

make a name for yourself also make your name

behindthehustle.com -

to become well known and respected for doing something in particular She would have done well in any sport, but Virginia ended up making a name for herself in soccer. The French director made his name in the 1980s with off-beat movies.

If you 'make a name for yourself' you do something that 

makes people notice you or see you as important.

It was with his third novel, 'The Darkest Hours', that he made a name for himself.