Is 301 redirect good enough?

Hi
The website removed it`s masking so it is using
"myhost.mywebsite.com" with a permanent redirect from "myname.com"All links to the website are "myname.com" Should all links from now on use "myname.com" or the full address? I imagine I should mask "myhost.mywebsite.com" but on the other hand a 301 redirect is good enough? I am wondering if in this situation the 301 will cause the index to use the full address while the short domain links to "myname.com" will build PageRank etc? Do I need to canonize the pages? i.e "myname.com/about.html" to "myhost.mywebsite.com/about.html" or masking with forwarding can solve this whole issue? It seems like the redirect 301 works flawlessly and Google treats myname.com and the long versions the same... Is this possible? Same goes for all of the other pages?