Me personally, my Gaming company would be named "Gubokon" reason for that is because it's name sounds so ridiculous that people would look into it. And I would Partner with Nintendo because of they're AMAZING success with EVERYTHING

If I could make a gaming company I would call it Szor Inc just because it looks cool, and I would partner also with Nintendo because they have the handheld system market corned as well as they make/own huge franchises like Pokémon Mario and Zelda.

I would call the series monkari and the mascot would be Marty the mongoose it would be a action RPG and I would partner up with Sony since I'm pretty sure Nintendo couldn't pull it off.

It would be called Sucka Free Inc. Most of the games would be Action, fighting, RPG, and all 3 in 1. Would mostly partner with Sony. The biggest project would be a Pokemon clone, but more adult themed franchise. 2nd would be something similar to the Mega Man Battle Network series. Then branch into a couple childhood cartoons in 2010's setting.

I would take a collection of Anime Characters by one company (Who ever "Streemline Pictures" did business with. Who ever "Orion Home Video" did business with. Or who ever "Manga" did business with.) and strike a deal with "Tamsoft" video games and build a Franchise from there.
You can make "spin offs" or dabble in genres or even experiment by mixing genres.

Editing and adjustments would be a breeze if the demand for a particular "Target Audience" were to change from one day to the next. (That is the beauty of Anime when comparing it to live action or hyper realistic graphical Stories.)

Take for Example of the fine line between "T" for Teen Rated Games and the "M" for Mature games.
The rules on the ratings change from one game to the next. It is almost as though there are no set standards. (Makes one wonder.)

In any case if the characters or plot line needs to be altered due to particular details like harsh language or the clothes are too revealing or the gore is too graphic or themes or suggested themes need to be altered? It would not be hard to alter the material and keep the spirit of the tale and characters true to who and what they are.
(There are allot of things Anime shows can get away with without conventional items. Example? if a person is shot and there is no blood? People still accept the character is hurt due to performance. Or visual ques like the injured area causes character to flinch or show pain. The Classic Bandages covering the wound in the next scene still works for some odd reason. Etc. Etc.) You can do all sorts of tricks that can help get the story made and done and have a game to sell by deadline. Regardless of the Rating. (Bonus Idea: have different rated Stories and multiple endings to unlock. Would work well with bonus material like outfits and weapons and even levels. Note: The only way that can work is if it was not D.L.C. But included on the game anyway.)

Anyway.
The game I would make?
I would start with an action comedy and go from there. I dig the "Dirty Pair Project Eden" so I would probably do a game based on that universe to start with my first game and go from there.
The First character you play through could be "Carson" from that movie. His Story.
It can be from the movie directly or a different tale all together.
Either way. I would have multiple characters with independent stories to unlock. Some characters have exclusive levels that others will not have access to till they are cleared at least once on normal difficulty. (Yes, we will get the "lovely angels" but I first want to establish the universe and the world. They function in.)

As far as what kind of action game?
Combat System?
I think I could borrow from "Tamsofts" "Onechanbarra" and mix it with a little "Tokyo Beatdown". The combat systems in those games are great and the Camera manipulation from Onechanbarra is near perfect.
They just need a little hint or sense of Platforming (Could be as tame as "Konami's Metal.Gear." Platform system. Character can crouch, dive and mount a ladder. The Majority of the time.) Yes the girls can jump and double jump in "Onechanbarra" but they almost never interact with their environment. (Not even to platform jump.)

After that we would need to address the vehicle stuff very lightly. Like Maybe A few more levels than "Super Star Wars" for "S.N.E.S." but NOT as one of the main features like "Saints Row" or "Mercenaries". (That can come in the second or third game.)

First things first. Establish the world the characters are in.
Give them level by level structure for the first game and expand on the world and character roster in each new game.

Eventually there could be a sandbox game in the future if the series does well. But I would have to make it more interesting than "Crackdown 2". (Might be why few do sci/fi themed sandbox games. Can't imagine why. I would love to steal the Millenium Falcon", or Rob the Cafeteria in the "Death Star.".. Then Survive Escaping.)

For now I would want to make a game with the same action as Devil May Cry or The Force Unleashed or even Metal Gear, But with an original story.

Do a few Extra things like "Vehicles" or "Resident Evil" Style "Key/Door Puzzles".
Maybe even do a few "Lockpick" sequences like in "Dead To Rights". Have a few "Stand off" Moments like the ones in "Stranglehold".
The list goes on and on for the possibilities.

If no developer would go for anything that is not tried and true? I would have to put my ideas on hold and put the characters I want to work with in a fighting game. (Same as everyone else.)
Good Luck.

Good Luck To All.
I'm done. Stick a fork in me.
Peace.