As mentioned in some of the previous posts, central pressure is not the key factor. For example, recent TC Vania was a low for a long time with the pressure down to 988hPa before it was named.
The WMO definition of a TC is "a non-frontal low pressure system of synoptic scale developing over warm waters and having a definite organized wind circulation with a maximum 10-minute average wind speed of 34kt or greater near the centre".
Sea surface temp >26.5degC is the generally accepted criteria for "warm waters" and it is also true that they usually need to be further than 5deg from the equator.
Different parts of the world do have different ways of naming and categorizing TCs.
What becomes interesting is when they move out of the tropics and head towards NZ (or parts of Australia further south). A TC has a structure quite different from a mid-latitude (or polar) system, with a deep warm core. Once they move south, as well as moving over cooler seas (or land), the jetstream usually becomes influential in shearing the TC and weakening it. Sometimes, the remains of a TC can become re-invigorated by the jet. But the structure will be quite different from the structure of a TC. Interestingly, TC Wilma kept its TC structure much further south than what we would usually see. I guess the thing to keep in mind is that they may be re-classified (ie lose their name) but can still be a major weather system.
Phew, that got a bit long