Here are some names of real secret societies. I find that when I'm trying to name something like this, I look to what's already out there and make something that similar but different so it's still believable. You might also try mixing up parts of different names to make something new.
1. The Rosicrucians or The Rosicrucian Order
2. Ordo Templis Orientis or Order of the Temples of the East
3. Hermetic Order of The Golden Dawn
4. The Priory of Sion
5. Knights of the Golden Eagle
Another thing I like to do is make up a name that sounds cool then translate it into Latin. Almost everything sounds smarter and cooler in Latin