There's nothing wrong with the name, Karen. I hadn't heard there was anything 'funny' about it except on here so please pay no attention. In real life I doubt anyone thinks of it.
Some years ago, 'Sharon' was the name people took the mick out of despite it being a Biblical Hebrew name; that stemmed from 'Birds of a Feather' but even people who'd never seen the TV programme were making fun of the name. Not much fun for those called 'Sharon' and extremely rude.
What does surprise me is that your name was so rare during your school days, I've known loads of Karens. 'Katie' isn't a name in itself anyway, should be Catherine or Katherine or Kathleen,shorted to Kate or Katie (which I do like).
Well here's a surprise, I looked up the meaning of 'Karen' - which is nice - and had no idea it came from Katherine:-
"Karen Origin and Meaning
The name Karen is a girl's name of Danish origin meaning "pure".
Karen is a Danish diminutive of Katherine, an English name derived from the Greek Aikaterine. The etymology of Aikaterine is contested, but generally considered to have arisen from the Greek root katharos, meaning “pure.” Kaja is a related name, as it is another Danish variation of Katherine.
Karen, a sweet good-girl Danish import, was so popular during the baby boom (Karen was Number 3 in 1960) that it's locked firmly into fashion limbo today. Recently, the name Karen has been turned into a meme, representing a hostile white woman—one who usually wants to speak with the manager.
Parents who want to honor a Karen or choose an updated version of the name might want to consider the Irish Kieran, the Cornish Kerensa or Kerenza, or variations from Karina to Kyra."
The meme is horrible. I wish it could be stopped but, honestly, I doubt is as widespread as you think.
You have a charming and feminine name, enjoy it and pay no attention to ignoramus.