There’s all kinds of stupid things that come in threes, but they aren’t really names. Fold, Spindle, Mutilate; Shampoo, Rinse, Repeat; Lock, Stock, Barrel; Hook, Line, Sinker, and so on. They’re not names.
I’m thinking more along the lines of Carolina, Virginia, and Dakota.
Or maybe Autumn, Summer, and Winter?
Of course there’s Abraham, Martin and John.
Of course, if you’re cruel or just… well, bent, you can have even more fun with this. Like naming your sons Hamlet, Othello, and Steve. Or calling your daughters Faith, Hope and Jennifer.
Huey, Louie, and Dewey, of course.
ETA: Dang! Kaylasdad99 beat me to it. I WAS surprised no one had said it yet!
Athos, Porthos, and Billy.
Tony! Toni! Toné!
Actually, if I wanted to be really really evil, I’d go with three nearly identical names:
Marie, Maria and Mariah (girl, girl, girl)
Jessy, Jesse and Jessie (girl, either, girl)
John, Jon and Joan (boy, boy, girl)
Tony, Toni, and Toné (boy, either, boy)
Morris, Maurice and Maury (boy, boy, boy)
Seeno, Hearno, Speakno. Of course, you would have to be evil to do so…
I always liked the idea of twins named Constance and Patience. You could add Prudence for the third.
I have triplet cousins who were intentionally named with names beginning with A, B, and C.
And then you can call them all “honey.”
Like Ivan, Sean, and Ian?
Albert, Isaac and Charles for boys. Marie, Rachel and Jane for girls. All famous scientists (Einstein, Newton and Darwin and Curie, Carson and Goodall) but simple enough names that most people won’t make the connection.
So the fourth would be Moles, and the fifth Ideal Gas Constant? 
Nah… not similar enough. More like Eve-Anne, Yvonne and Ivanna.
points finger at Mahna Mahna
You’re a Duggar! I just know it! 
Myshack, Yourshack and Abungalow.
Darn. And here I thought I’d fly under the radar because I didn’t use any Js. 
(Joy-Anna, Jana and Johanna… Oy!)
Alvin, Simon, Theodore
Maddisyn, Keightlynne, Makaylla
Anne, Charlotte, Emily
You’re a goddammed genius.
Nah, they’d have to be named Jeve-Anne, Jyvonne, and Jivanna.
That is very true. But not because of this since I didn’t come up with it. 