Perhaps I can shed some light on this.
Domain registrars simply maintain the list of domains. They charge anywhere from $8.95 per year (godaddy.com) to $35 per year (netsol.com, the original monopoly registrar) PER DOMAIN and everything in between. They are simply the recordkeeper for domain information. If you're happy with your registrar's price, you don't have to change registrars when you move who hosts your website. It just happens that Dreamhost is also a registrar (Domainatron).
In the Dreamhost webpanel, you'll need to add your domain there. But, that still does nothing until you ask that nameservers be updated. Make sure you upload to your Dreamhost space before proceeding on...
Now, where you're currently hosting (yahoo) you'd need to login (http://domains.yahoo.com/) and change the nameservers to move away from yahoo. Now, because I've never hosted with yahoo I can't tell you the specifics. And, because you've initiated a registrar transfer (tucows) to somewhere (Dreamhost Domainatron?) you may need to login there instead to update your name servers.
An example of one of my many domains follows:
Years ago, I registered a domain (pics-by-jim.com) with Network Solutions; then the only game in town. $35 per year for the single domain. I hosted with my employer at the time, an ISP in Ohio (Zoomnet) for free because I was staff.
Earthlink bought Zoomnet and we all got the boot. (No humans required.) I signed up with Dreamhost. I logged into the control panel and added pics-by-jim.com as a domain. I uploaded my webfiles to my Dreamhost space. I asked Network Solutions (my registrar) to change the nameservers from ns.zoomnet.net, ns2.zoomnet.net, etc. to
I acknowledged all emails from Network Solutions that prevented someone from moving my domain without my permission. It may take 3-4 days for a nameserver change to be visible throughout the world to everyone. (Some in that transition time were seeing my site still at Zoomnet; others were seeing my site on Dreamhost.) (Which is why you're wise not to cancel your yahoo webspace until say "a week" goes by.)
Later, I tired of paying $35 per year when I could get it for $8.95. So, much later, I went to godaddy.com (a registrar) and ask them to become my registrar. They asked Network Solutions who eventually realized they were going to lose my business and godaddy.com became my registrar.
Sorry for all the gory details. If you tell me your domain name, I'll look and see who the "whois" record says is your registrar and who it says your nameservers are.
Feel free to email me privately at firstname.lastname@example.org or write back here with specific questions. (Or, of course, write Dreamhost support.)