“Can I get change for a twenty?”
You have a twenty-dollar bill, but you need 20 one-dollar bills instead. You go to a bank and ask the teller this.
Can I get change for a twenty?
To "get change for ___" means to give someone a large bill, and get lots of smaller bills or coins in return.
You can say "change for a twenty". Or, if you want to be more formal, "change for a twenty-dollar bill":
Could I have change for a ten-dollar bill?