I thought Facebook was forcing people to use their real names now? I tried to change my last name on Facebook a couple years ago, and it wouldn't let me, because it wasn't my real name. The only people I see with not-real names now are ones who registered with those names.
Check their specific policies here: www.facebook.com/help/112146705538576
I have a 'creeper' account with no friends or info that I use to look up info on businesses in my area, what with how many companies stopped having a website and just use facebook now. I had no issue signing up with a 'fake real' name, exs. Sarah Smith, Anna Garcia, Jonathan Jones, etc. As long as your name complies with the rules and isn't overtly fake, ex. Jane or John Doe, the system automatically approves it. You can also change your name at any time, but only if it complies with the rules listed in that help article and only once every 60 days. It does seem to require a last name be shown now, but a lot of people I know have just opted to use their middle names instead or even break their first name into two parts, ex. Marianne to 'Mari Anne' and so on, with the second half in the surname field. In general, it seems only extreme changes to the existing name trigger facebook's system that requires you to submit an ID, so get a bit creative with your real name and you should be fine.