For copyright, there is no legal requirement that the work be registered in the legal name of the author. Not registering it in the legal name of the author would, however, be disadvantageous. The whole point is to prove that you own the work and are therefore able to pursue damages or cease and desist orders. Registering under a name that is not your legal one adds one more complication to a complicated situation.
If you own a business, checks can be made out to the business, though you would certainly have to sign checks and contracts with your legal name as the chief or sole proprietor of your business.
So, if you call yourself "Edmund DeVere" when you write screenplays, you can establish a loan out corp. called "Edmund DeVere Inc." If a prodco buys one of your scripts, they can make the check out to "Edmund DeVere" or "Edmund DeVere Inc." This is only worthwhile if you're making substantial amounts of money. You'd still have to endorse the check with your legal name, and use the same to sign contracts.