Changing the _cfuid cookie's domain

I need to make a change of _cfuid cookie’s domain because it is appearing on other sites with different subdomains. I know that the cookie’s domain is automatically set according to what domain is registered. Right now the cookie’s domain is set as sitename .com but it needs to be changed to www.sitename .com. It there any solutions in Cloudflare’s dashboard or does the domain need to registered as www.sitename .com in order for the cookie’s domain to be changed accordingly?

I had to put spaces in url examples because you are not allowed to put more than two links in a post as a new user

This cookie is only for Cloudflare’s use and helps prevent bots across the internet. Curious as to why you want it moved? A cookie on www.example.com vs example.com won’t make a difference in terms of speed or reliability.

If this is for a speed test / security report, you should skip this recommendation since it doesn’t impact either.

So you want the cookie to be valid only for one host, but not domain-wide?

I am afraid that wont be possible to customise. Maybe if you are on an Enterprise account, but I doubt thats what you want.