You actually you get some ley way when you use you own name.

Like Patterson Games, because it is my legal name it can be used by me, even if there is a Patterson Game somewhere else. Confusing and probably not practial. But there are many Disney business's that are not part of the Disney Corp group, this is because, the person who owns the business has a legal name of Disney.

RA Games is boring.....

If you are going to be focusing on Noah related games why not try something to do with the Noah story.

Big Flood Games, (Ha, I love the term Big in company names.) (BFG.... Now thats funny)
2 by 2 Games
Ark Studios
Big Ark Studios
Noah's Ark Studios
40 Day's Studios

Have some fun with it.

You are free to be Alaimo Studios / Games....

Go for something fun....

Ken