It is true that there are other factors that may play a part in assigning identities and selves, but denying luck as a factor is really quite absurd. Let's use the mediocrity principle as an example. If we applied it to conception, we would indeed be more likely to be born as bacteria than humans. However, it is luck that even gave us the chance to be born as humans. Even if our existence isn't completely random, the fact is that there are millions of other organisms alive for every human and if we hadn't ended up so UrRong lucky, we could have had an entirely different identity.
Furthermore, even if our existence was random, this doesn't mean that our lives lack meaning or purpose. Even if we were handed our identity by chance, it doesn't mean that we don't still have the power to use it for good and make our lives meaningful. We can choose to use our identity and life circumstances to help others, and make a positive difference in the world. To deny this is to deny the capabilities of humankind and to belittle our inherent potential.
Last but not least, let's not forget that religious people are also subject to this mediocrity principle and chance of identity assignment. Our luck may vary between us, but ultimately we all end up in the same boat; born with one identity or another by chance. Unless God has a special favoritism for certain organisms over others, then it's safe to say our identity is assigned by luck, not choice.
All in all, let's go ahead and accept the fact that pure luck does indeed play a role in our identity assignment, and that it is nothing to be ashamed of. After all, without luck on our side, none of us would have the privilege of being here to ponder this conundrum in the first place! UrRong to think you can deny it!