I often create BBEGs as characters in D&D Beyond. I can't seem to add them to the campaign or encounter without my players seeing them. It would be a bit of a giveaway for them to suddenly see "(Name), 10th level Wild Magic Sorcerer." Am I missing a way to do this? It would also be nice for the CR calculation if the evil character could be counted on the other side of the equation, but this isn't as essential as the first bit.

The CR calculations don't have any allowances for enemy characters. They're designed for characters on one side, monsters on the other. If you're not using CR calculations, the concept of "sides" doesn't matter.

Also, characters don't make great opponents. They're balanced differently, and don't have anything like the staying power, and dish out way more damage. Compare the various humanoid monster stat blocks with equivalent-level characters. You're better off building your foes as monsters.

What I've sometimes done is build them as characters, and then use that character to inform the homebrewing from a humanoid stat block.

Honestly, I ended up creating a separate campaign (and titled it “Campaign Name [NPC’s]” so I can have them as a reference but not let my players see it. 

When it comes to adding them to a map, I plan to duplicate the character and make them a level 1 (class).  

I think DM’s should be able to hide their characters though in the campaign itself. 

You shouldn't be using the character builder to create NPCs, that is what the the Create Monster feature in the Homebrew section is for. Monsters and NPCs work differently than PCs.

Thanks, folks! These are good tips. Right now the NPCs just exist among all my other characters. At least I could drop them into their own campaign, as helloitskeetie suggests. 

I still feel that D&D Beyond should be flexible enough to give me the option, though.