If you are selling products or providing services to others for profit (as opposed to being employed by someone), you are a business. It doesn't matter whether you have a business name, specific bank accounts, or file your taxes as such. It doesn't even matter if you don't make any money doing it. You are still a business.

Well, irrespective of whether you set up as a proper business or consider this a hobby if the income derived exceeds $600 for the year you are to report that on your IRS tax return.

That said, this is about the point when an entrepreneur will decide if they want to pursue this as a real business. That is, not that it is not a business now, but whether you intend on investing in this for the longer term. If so, I suggest setting up a proper limited liability shield such as an LLC (this also has some tax advantages) and also conduct the proper trademark clearance on the name and file an application with the USPTO to ensure that you are not infringing on someone else and so you can own the brand under which you hold yourself out to the public.

I will link you to some general helpful info below and suggest you contact a lawyer in private to discuss your plans. Most of us here, including myself, offer a free phone consult so you may want to take advantage of that.

Best regards,
Frank
Natoli-Lapin, LLC
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You may take it for granted that your company is a "small business."

Licenses, permits, zoning laws and other regulations vary from business to business and from state to state. You will need to consider requirements of the Americans with Disabilities Act in order to accommodate needs of your customers

It certainly sounds like you are operating a sole proprietorship. I'd look around your area to see if there are any workshops or clinics available for start up businesses that will be able to help educate you on the legal and accounting requirements for your photography business.