Out of curiosity, why do you think putting "Games" in your name is a bad idea?
Inserting specifiers into a company name detracts from the title (eg: Nintendo Games) and creates a hobbyist/indie vibe. Since this is so common among new and "independent" businesses, inserting them makes your company seem as part of the "void", or vacuum. In addition to creating an Independent vibe, "Games" is also a specifier that is strongly associated with Small Businesses--Neither of which have good connotations. Small Businesses and Independents are typically viewed as individuals with whom others have some camaraderie with, while Larger Corporations (such as Nintendo, Microsoft, etc.) are viewed simply as "corporations". People view Larger Corporations in a generally higher esteem, whereas they view Independents as equals. Many people feel some form of elevation upon purchasing a product from a Large Company--of any kind (bragging over shoes and games is common among adolescents), while others may have feelings of condescension or entitlement from purchasing a product from someone they view as equal. As people begin to feel they have a "closer" relationship with you, the individual, they begin to request more for less, under the assumptions that they have a greater degree of control.
I myself have noticed this; back when I made the novice mistake of marketing directly, I got little business and no progress, however, after learning the game and talking through my company, I noticed immediate and consistent improvements in both sales and customer satisfaction.
That's the main point; Mystification. Adding "Games" not only removes this important quality, but it also consigns the company into the void, filled with countless others who have done the same.
It also shows indecisiveness, or, as I call it "Indiecisiveness", subconsciously, it creates the vibe that the creator themselves are unaware of their goals, and include "Games" as a form of reaffirmation. In a world with increasingly strict consumers, being anything short of perfect is unacceptable. This is also bad for merchandising; what if a company
does see some potential in their products and decide the make toys of them? completely disregarding their designs, seeing "Wavedash", let alone "Wavedash Games" imprinted on the box would probably incur more giggles than actual sales.
Simply not including "Games" isn't the sole solution, however. The name itself must also be satisfactory, whether it be meaningful (Nintendo, Microsoft), or memorable (Nintendo, Microsoft, Apple, Facebook, Twitter, Snapchat, etc).
To reiterate and compliment my past points, if you want to rival Nintendo and similar companies in success, your primary goal should be to distance yourself as an individual from your company as far as possible. I'd advise hiding your name for as long as needed, avoiding interviews at all costs until you're successful, and prohibiting (or strongly advising against) staff or relatives from mentioning your name or anything about you until you've reached a level of success to where it will no longer affect you. I'd advise asking them to deflect the question rather than responding with refusal, as you want to appear "mysterious", not "hostile".
Initiating with 3D Games is also a good way to establish yourself on the positive, as most indies use 2D for either aesthetic or financial reasons, creating an immediate distinction which can be used to propel you to greater levels of success. If you really want to be extravagant, make a custom engine as well (assuming, of course, these are all of quality), or at least use one of the most sophisticated ones (Smash runs on Havok, I believe).
Ultimately, it depends on the level of success one wants to achieve, some people may prefer to live a standard middle-class life, complete with the camaraderie that comes with Small Businesses. Others, however, may aspire to rival or even eclipse the success of those like Bill Gates and Mark Zuckerberg. Neither one is
wrong, just
different.
tl;dr - Adding specifiers (in particular Games) shows uncertainty and creates the appearance of the creator being a Small/Independent business, which aren't taken very seriously in the world. Perhaps Bandai Namco Entertainment is an exception, but that's only because they are an established company of which existed at the dawn of video games. Prior exclusivity and being established gives these companies automatic advantages, however it's not impossible to rival them even today if you have the necessary knowledge and skills.
Melee's still better 
