trading on someone's name

[Mike Hussey]

Linus: Oh, he didn't tell you? He doesn't want me trading on his(Linus's dad) name.
Ocean: Do this job, he'll be trading on yours.

What does "trading on someone's name" mean?

Source: Ocean's Eleven (a 2001 American heist film directed by Steven Soderbergh and written by Ted Griffin)

 

[Tdol]

Some say that Eric Trump and Hunter Biden trade on their father's names. Many people would not find it easy in either case to list what they have achieved that was not because of their names and connections.

 

[emsr2d2]

He doesn't want me trading on his space here (Linus's dad's) name.

Remember to put a space before an opening bracket.