I am going to submit 5 visual novels in a series and need to know if I should use the pen name used with the novels or my own name.

depends. if they accept the game you need to go into a contract with them, and they need a person to pay the % of the sales. so if your pen name is recognised as a legal entitiy, then that is fine, if it is not then it si more complicated

You're trying to enter a business agreement. Would you use your pen name when buying a car or applying for a credit card?

Type in whatever you want displayed as Developer/Publisher on the game's store page. If it needs to be your real name, they'll let you know when working out the details after accepting your submission.

There's a difference between submitting your game to GOG and actually getting into a contractual relationship with GOG.
For the submitting part alone, your "pen name" should suffice (else the "submit your game" template would mention it, I'm sure).

For the contractual relationship (if it should ever come to that), you'll need to sign all the necessary papers with your real name, of course.

That's because businesses don't tend to do legal business with partners, who sign their contracts with "arsefart69", if you catch my drift.

Only exception to that would be (as amok has mentioned) that your pen name is legally registered (think Richard Bachman, alias Stephen King, etc.)

Pen names are too modern. This is gog, where we have old games, so I think you should use a pencil name. Maybe even a stylus name?

Pens aren't modern.

Quills are a type of pen, but whatever.