It's unclear what you mean by "DNS alias name".
The "Primary DNS suffix" is used by the computer to resolve unqualified names. If, for example, you issue the command "ping bob" and your primary DNS suffix is set to "dobbs.com", the DNS resolver will search your HOSTS file for an entry for "bob", then an entry for "bob.dobbs.com", and finally will issue a recursive resolution request to your primary DNS server for the name "bob.dobbs.com".
Basically, the primary DNS suffix is appended to unqualified names by the resolver during recursive resolution requests.