My colleague, Jason Rudkin-Binks, is a specialist in this area and has answered your question:
There are really 2 ways that a business (trading) name can be protected. One is via a registered trade mark and the other is by that name being used in trade, i.e. as the name of a business, and so gaining a reputation in that name. Are any of the similar names you have found protected as trade marks? We suggest that you have a look on the IPONZ website which is located here. If so, then it is a question of how similar the trade mark and your name are and how similar the goods / services protected by the trade mark (not, not those actually used) are to your goods / services. The closer those 2 things are, the more confusion is likely and so the more likely your use will be infringing. In the case of the other similar name simply being used in trade, then it is a question of how close it is, how much use has been made (does it really have a reputation?) and of course, how similar the services it trades in are to yours. So the answer to this is very fact specific. In order to protect yourself, we suggest that you consider registering your own trade mark and also undertake the searches that Andy suggested and compare the services offered. It is perfectly fine for 2 businesses to have identical names provided that the goods / services offered are sufficiently different.