yes, everything is at DreamHost.
So I would create two domains at DH.
myshortname.com as a regular hosted domain and also
mynicelongname.com which is a redirect to the first domain.
Now that seems more complicated than my original goal of reducing the domain name in order to simplify. For example, previously I had a registration with GoDaddy and all I had to do was to set it to redirect to myDomainAtDreamHost.com
So does this mean that to simplify things all I need to do is to create a domain at DH called
mynicelongname.com, which is also registered at DH
And the internet will figure out the two are related.
Am I missing something?