I've only had this issue once. It was about my character Cirrus. They were part of a cast of cloud-based characters, so naturally they were named after the cirrus summer cloud.
It turned out there was a popular webcomic with a character of the same name.
Someone commented on my stuff saying "Ooh, some of the names are also used in this other comic" and I just... didn't really care that much. I considered whether or not it was worth acting on, but I realised that it's just a name. Nobody is going to devalue my character because of it.
I've got really dumb character names in my main universe though, like Increase Decrease and Satan Rapist and Jammin' Jivin' Coolguy (a girl! don't judge!) so I think the fact that my work is full of its own memes makes it even more unique and charming. Hell, I've got a thing where the phrase "gobshite" appears all over my canon in various different languages but never english.
I think memes shouldn't be something to hold you down - I think they can also work in your favour! Play around with it!
Also, Monica is a normal enough name that sane people won't connect it automatically. I don't think it's that much to worry about. If it was a more specific name then maybe...