My wife's name is Karen, and I've teased her about it over the past 6 months and she's kept mum about it.
She finally admitted to me that it gets on her nerves greatly and she resents all of it. It came as quite a shock to me (because I find I lot of it funny) but I suspect there are a lot of Karens out there that aren't amused.
The kiddos and I have now resorted to calling her "K-Dog" which she gets a kick out of.
I suspect that anyone who's caught grief for their name wouldn't be surprised. We (generally) don't choose our names, and yet it's imbued with a lot of our sense of identity.
I have a name that has been relentlessly mocked for the last 36 years. The suggestion by others to me has always been “if you don’t like people mocking your name, change it”.
So, I’d say the same applies. If people called Karen don’t like the new association with their name, they can change their name.
Otherwise, sticks and stones.
Also, they’re not the ones actually being mocked here - I get grief from grown-ass adults over my name, directed at me - so frankly, I think anyone named Karen who sees this as a personal attack needs to either get over it, or change their name.