You would need to change the nameservers the domain has at namecheap to ns1.dreamhost.com, ns2.dreamhost.com and ns3.dreamhost.com.
Once this has been done you can add the domain in the CP at manage domains > Add/remove domain.
Later if you stay with dreamhost it should be possible to not renew the domain that is wrong, transfer the domain fully to dreamhost and nominate the new one as the free domain.
You don’t need it to be nominated as a main domain any domain you have is basically treated the same as any other.
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