No - you only have to register if you are a Data Processor (or a certain class of Data Controller), not usually if you are merely holding data in the normal course of doing business. Even if you don't have to register, you must use that information only for the purposes for which it was provided and all the usual data protection rules apply (keep the info updated, delete when it's no longer needed etc).
Whether you need to register if you are only a Data Controller, is outlined on the Data Protection Commissioner [broken link removed].
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