Whether or not Louis decides to accept either of your payments without screenshots is up to him. I'm assuming he will, since you both seem trustable fellows.
However, anyone who does not submit a screenshot from this point on will not have their payment accepted.
Meaning, if you don't know how to take a screenshot, PM Louis and ask him. DO NOT send Louis any gil until you know how to do it! Test it out first and make sure you know how to take a screenshot.
There's no way for him to legitimize your payment without the screenshot, so DO NOT send him any gil unless you can provide him a screenshot of the "Successful Payment" screen, otherwise you'll lose your gil and have to pay him again if you still want the name.
By the way, you take a screenshot by pressing Alt + Print Scrn. Now no one has an excuse not to take one.
If you have any problems or questions about the payment procedure Louis outlined, privately message him or reply to this thread.