Nope. No worries. I've done it, and it makes no difference to Uncle Sam how/where you manage your inflows and outflows. It's all the same for taxes.
Your bank might have a problem if you are Joe Smith and your checks say New World Exterminators, but then again, who is actually looking? You would just put your name first, then the business name (if you've got one).
I may be cavalier about the checks though, anyone out there in banking who can address this?