I use siteground as my host and I they told me I need to have https://www on my website for Cloudflare to work. I don’t want to do this as I have 2 websites that were set up for many years that are https:// and have multiple backlinks/listings etc with the non-www version. I have my domains with Siterground as well.
Any suggestions on what i can do without changing anything and still using Sitegrounds Cloudflare Plus option.
You need to contact your host about that, as you are on a partner setup and your host manages that.
However in your current setup you are unlikely to get it to work on your naked domain. Your best bet might be to disable Cloudflare on your host’s side and sign up for a full account on Cloudflare directly.