The answer here is 'perhaps.
A trademark, by definition, is a sign that one trader uses to distinguish their goods/services from those of other traders. A personal name is no different to any other trademark in this sense - it must be capable of distinguishing in this manner. So, if your name is common and other people may need to use that same name in connection with similar goods/services then it could b e more difficult to register. However, if this sort of issue is reported to you by the government office there are ways you may be able to address the issue and ultimately gain registration/protection.
The other thing to be aware of with registration of a personal name is that if you happen to share a name with a famous person it could be more difficult to register. For example, if your name happens to be Shane Warne and you try to register your name in connection with sports apparel/products this could be difficult - it could be confusing to the public as they may assume the products are endorsed by cricketer Shane Warne; you cannot register a trademark that's going to confuse/deceive in this manner.