No, I mean you don’t need to move your domain between registrars, but you will need to update the NS records at Hover for your domain to point it at a different providers DNS to test this theory. At present they’re set to ns1.hover.com and ns2.hover.com
It’s a very quick and pretty painless process. If you sign up for CloudFlare then try to add the domain there they will give you two new name servers which need to be input at Hover. There’s a guide to the hover side here: