schlmoe said:
In addition to getting a PO box, you can also get a "DBA" form (Does Business As) from your state. I had one for a side business awhile back, and it cost me $10 (of course it could be different in your state). This allowed me to do banking, etc. in my business name. For models, you would be able to get mail/packages addressed to your stage name. You would just show the form when you set up the PO box, and you're all set. Of course UPS/USPS would know your real name, but it could still solve a potential hang up for you.
I would be very careful getting a DBA (also called a Fictitious Name in many states). Most jurisdicitons make DBA / Fictitious Name filings public and quite a few allow you to easily look it up online. For example a random one I just pulled up:
http://www.sunbiz.org/scripts/ficidet.exe?action=DETREG&docnum=G09033900603&rdocnum=G94228000082
Note that not only are their real names listed, but their legal addresses are as well. This could actually be worse than just avoiding the DBA altogether.
That said, you could certainly consider setting up an S-Corp or an LLC to provide you with some anonymity (and possibly some liability protection too, if you care about that). You'd want to consult with a lawyer on either of those options, however, particularly if you want to ensure that the entity is structured in such a way that your identity is really protected. And there are annual costs with maintaining corporate entities.