The idea of "non-self" is well developed in Buddhism. It is not to erase who you are. Rather, it is to not be attached to things that may and will eventually pass in order to be a full person. For example, when I became ill in 2004 I did not know that in 2013 I would have to stop working. I never dreamed of not being a doctor. If you'd have asked me, I would have said that it was my identity. I did grieve the loss of my career but yet here I am, still me. It took losing the attachment to this part of my identity as a doctor in order to see that there is in fact more of me hidden below my career. We do not need to stop anything. In fact, in some Buddhist teaching it is said that you must find yourself before losing it. This is ridding ourselves of the false self that Dan refers to. Ultimately, if you lose attachment to all things in the material world you become nothing, and in being nothing, you are everything. This is, in my view, what the Christian teaching is getting at. Live your life fully, but with complete knowledge that any part of it may be gone tomorrow. Therefore, do not development attachments to these things as something you could not do without. This is not easily accomplished. But living a spiritual life keeps you aware of your attitudes towards what makes up your identity and how much you are enslaved to these things. Free yourself from them.