Hi, I am currently using six for my website. If I change the web servers, will fix not ‘talk’ to 123reg?
I’m not sure what “Six” is.
Your title asks about changing name servers.
The general rule is that a site that works with HTTPS when Cloudflare is Paused (lower right corner of the Overview page for your domain at dash.cloudflare.com), the site will work properly when Un-paused and 
Proxied.
If you’d like more specific guidance, please post your domain name.
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