I'm not going to let my previous employer use my name that is still on their website
Do you want to erase your name from the website?
Yes, no one needs to know my name
Call them and explain the situation about your name being on the website. You don't work for them anymore and you have the right to pull your name out from their company website.
I would but I don't want them to think I want my name removed for any bad reasons. I just don't want my name showing up anywhere.
Taking their name out of your resume will harm no one but yourself. It's silly to not mention your experience with your previous employer for some stupid reason. You don't need to feel guilty about asking them to take your name out of their website.