But I don’t want to redirect to another domain. I want to create a new website with the domain I bought, so I create it on a subdomain of another domain I own, and use my new domain.
Sorry, your original question mentioned Redirect several times.
If you want some other site to respond to a different hostname via a CNAME, then that other site needs to be configured to do so. Some hosts even let you add multiple hostnames to a single site. You would need to ask your host how to do this.
Ok, so the problem must be on the destination domain?
I didn’t know the right word, if it is redirect or not, but it is from new domain (on cloudflare) from a subdomain in another host. I guess is what you said, the settings here are alright with the cname, but the destination domain doesn’t allow it.