Here are some basics:
A company name is the name of an incorporated entity.  Governed by uniform
state law called the Corporations Law and administered by the Australian
Securities Commission on behalf of every State and Territory.  Any
incorporated entity wanting to carry on business in Australia must be
registered under the Corporations Law.   Regular domestic entities get an
ACN (Australian Company Number).  Foreign and non-standard entities get an
ARBN (Australian Registered Business Number).
A business name is required to be registered whenever a person or company
wants to trade using a name OTHER THAN its own name.  Business Names
legislation is State based and administered.  A company or an individual
can own a business name.  It is only required so that anyone who wants to
know the name of the entity carrying on business under that name can look
up the register (= translate table) to see who the real entity is trading
using the pseudonym.  Registration of a business name confers no rights to
the name although it is impossible to register a name that is identical to
one already registered.
A non-profit organisation can also be incorporated under State based laws -
no ACN or ARBN is required for those entities but they usually will not be
looking for a .com.au domain anyway.
A trade mark is the brand name by which goods or services are known.  A
trade mark may be owned by anyone regardless of where they live but is
liable to be struck off if not used by the registered owner for more than 3
contiguous years.  A trademark may or may not be the same as a company or
business name.  For example, Commodore is a trademark owned by the entity
that we used to know as General Motors-Holden's Pty Ltd.  (I think it's
recently changed its name to just Holden Pty Ltd).  Oracle is a trademark
owned by Oracle Corporation.  A trademark identifies goods or services
rather than entities.
A domain name is normally chosen so that it is the most likely thing people
will think of when they want to find you on the web.  Most organisations
want to have a domain name that approximates their real name.  Some
organisations are more likely to be searched for by their product with many
people possibly not even knowing the formal name of the trading entity.
For those people a domain name that approximates their trade mark would be
appropriate.
In my view Melbourne IT (and any other current or potential NIC) should not
impose any requirement whatsoever on an applicant for a domain name and
should play no role in resolving disputes about names.  The safest approach
is for them to register on a first come first served basis, although
obviously if they form the view that someone has no motive other than to
hijack a name for ransom I see no reason for them not to refuse the
application.  This should be a sparingly exercised power, though.
If someone uses a name in trade or commerce and that is misleading or
deceptive because people think it belongs to someone else that will usually
be actionable under the Trade Practices Act and that is where the fight
should be held.  NIC's that want to set up dispute resolution mechanisms
and complicated thresholds for applicants are just buying trouble in my
view.  At the moment no-one can demand a domain name but it won't be long
before a refusal to register a name is challenged and we may see some
interesting law as a result!
Philip Argy
Vice President
Australian Computer Society, Inc
Chairman
Economic, Legal & Social Implications Committee
ACS
Head
Intellectual Property, Trade Practices & Technology Group
Mallesons Stephen Jaques