Try adding new one like this.
Open recorded invoice from your "Open Invoice List"
Change the Sales Person, by typing in the new name you want and record the invoice again.
Shut it all down, open it up and check if new name has stayed. You can then put the other invoice back to the correct name also.
I've just tested it and it worked for me.
As far as deleting/altering current Salesperson name I have to agree, you can't!