Other random customers won’t know who you are, that’s true. But what about your friends and acquaintances that you have referred? As soon as they see your username in the list they will know exactly who it refers to.
And if you’ve done particularly well in the list you might not mind one or two close friends knowing but if everyone knows and they talk, you could quickly find yourself the subject of local gossip. That could get awkward and not enjoyable!
Do you see where I’m coming from?
I think Will’s suggestion of letting you know your rank is a good one. And there’s no harm in displaying the totals of say the top ten or twenty. It’s just the automatic inclusion of usernames that might cause a problem - although as I said, people could opt-in to have their username displayed if they wish, but that should be their choice.