Here in France, only small cuddly pets are given Mignon as a name. Eventually though, even animals outgrow it and are renamed. My mother-in-law's once cute little kitten grew to become a fat bad-tempered demon who hisses at everyone, so he went from being Mignon to Timimi, with the only vestige of Mignon being the -mimi at the end.
I went to school with a girl named Mignon, but she always went by the name Mindy. One day I asked her how she came to be called Mindy because it's nowhere close to the name Mignon. She said when she was little people would butcher her name so much (mig-non), she insisted she be called Mindy because it was simpler and people would pronounce it right every time. When she turned 18, she changed her name to Mindy.
"Mignon" is masculine; "Mignonne" is feminine. Plus, not many non-French speakers would know what "mignon/mignonne" means and associate it with the steak; I still think of the steak, even though I speak French to a degree. And naming somebody "cute" sounds a bit odd (with exceptions to "Bella", "Linda", "Callista", "Alan", and the like).
It's hard, as a child, growing up with a middle name that you can't even pronounce. It wasn't until I was in fifth grade that I learned how to pronounce it. Then, in high school, I learned that this is actually the masculine form of "cute". But no one in America's going to know. I really appreciate having this as a part of my name now simply because I have never met another girl with a first name of Mignon. I never got the "filet mignon" joke, though. I always had people pronounce it as "Mig-non", which drives me insane.
It's a weird name from anyone's point of view who has taken French or speaks it. I took French for three years in school, and this word came up several times. Many people would surely mispronounce it, and it doesn't sound all that cute that way.