I haven’t used Square for training but my partner has used it for her art business.
You can use the same business credentials that you use for any other part of your business. Whatever you accept checks as, you can set up the Square account. If you take them to your own name, set up the Square accordingly. If you have a DBA or operate any kind of LLC or other business, set it up for that name.
Square will take a small percentage as a fee.
Then they will provide you with receipts/invoices/etc.
You will use these the same as anything else.
If you’re operating as a sole proprietor, I believe you have to report the full charge on your schedule C and deduct the service fee. But don’t quote me on that, I’m not an accountant.
If you’re an LLC or corporation or anything else, just use the receipts the same as you would any other.
I assume by your question that you’re a sole proprietor, so, no you do not have to be a business to use Square.
As to your question of if it is worth it, the answer is probably. If you believe you will have more clients, and/or retain more clients, etc by being able to accept cards, then yes. If you charge $50 a session, you’d pay around $1.50 in Square fees.