There are several ways to accomplish this, but the DNN portal alias has nothing to do with it.

Since your "vanity" Url has no file extension, you would first need to setup the infamous IIS wildcard mapping, which obviously won't work in a shared hosting environement as you most likely don't have access to IIS to begin with. But if you are able to configure IIS that way, you could use a module such as Url Master to do the actual redirect.

Or, and that's the method I prefer and use on http://seablick.com/blog, you could install a 3rd party IIS extension like ISAPI_rewrite and have it handle the redirect on the IIS level. But again, for that you need access to the OS and IIS.