The closest that come to mind for me are the DelRubio triplets.
There is now a page on Wikipedia listing American Triplets (I didn’t come across one for the rest of the world.) 3 sets are listed that have show biz fame which haven’t been listed yet.
The Kane Triplets. Singing group of the 60s-70s. One of them was murdered in 2007 by her cop husband.
The Levesque Triplets. Apparently “personalities” mainly.
The Taylor Triplets. The are a YouTube/etc. (in)famous group called Taylor Red. (They have red hair.)
A couple years ago there was a YouTube video posted by a guy trying to figure out how in Aunt Maude’s spleen are these people “famous”. View buying is a major suspect.
Just to remind people of the point of the question. The OP doesn’t want sets of performing triplets, whose fame derives largely from the fact that they are triplets. He wants people who have achieved fame in some field, and has two siblings who are largely unknown.