We need a company name clinic here. Giant Mook sounds good, too. I first pictured the MOTHER mooks, as in alien mooks.
I think Smithy is right about Giant Mook. If you're familiar with common gaming slang, it's a great name, but if you aren't, it sounds like an insult. In other words, it's great for those who visit tvtropes, but not for people who visit urbandictionary. It's better to find a name that has broad appeal.
Aliterate! Big Boss!
Probably taken, but you get the idea.
Metal Gear Solid did it first.
How about 'Hidden Boss'? It sounds a bit better than Secret I think
I agree. Thanks to everyone who suggested it. If I go this route, that's the name I'll use.
It looks like I'll need to do some more brainstorming before I can decide on a name! Thanks to all who replied, and sorry to disappoint.