For example, the name 'www.yahoo.com' is actually '64.58.76.179'. Seem confusing? Don't worry. All you really need to know is the names. The computers will do the translation into numbers.
The allocation of names, and the conversion of names into numbers is controlled by the ICANN, The Internet Corporation for Assigned Names and Numbers. This is an organisation that anyone can join to express their opinion on the running of the internet.
You can get an idea of how open to public input the ICANN is by clicking here. This (rather long) document will indicate how often the global public are consulted about changes.
While the ICANN looks after the naming principals, the IANA looks after the allocation of numbers to the available names. The Internet Assigned Numbers Authority make sure that no two people can have the same name for their computer networks. After all, there should only be one Coca-Cola, right?
In all countries the assignment of the names for that country is governed by the same rules given out by the IANA. In Ireland the assignment of numbers is controlled by the Irish Domain Registry. For a list of all countries, you can click here.