Website Name -Want to change

I jumped in on the 77c/month deal Dreamhost had & quickly thought up a name, now I have a better one. Can I register this new name & then transfer it to the 77c/month deal? I hate to spend all this time on a website that I’m not happy with the name now that I’ve come up with something better.

all plans can host more than one domain, just register it, set the nameservers to DH’s and add the domain via the web panel. You might want to set it to “mirror” the site you have up now if it would be too big a hassle to move the site to a new spot