Lawyers are traditionally (and, in many jurisdictions in the US, still are) required to operate as either sole proprietors or partnerships - both are business forms (as is corporation), but unlike Corporations, Limited Liability Partnerships, and other forms, neither Sole Proprietorships nor Partnerships afford shelter from personal liability.
If I sell stock to raise start-up capital, and my great business plan doesn’t work out, my shareholders can lose the money they paid for the stock - but the creditors cannot go after them for the business debts.
If I set up as eithe a sole prop or partnership, I /my partner(s) and I are personally liable for debts of the organization - if I screw up that contract and my client loses money as a result of that error, I am PERSONALLY responsible for those damages.
Accountants are, traditionally, treated the same.
This is why E&O insurance is a really, really good idea for those folks.
I suspect that the same thinking of holding them personally responsible is what requires them to use their personal names as business names.
Trivia:
Next time you see a letterhead of a law firm, you will (usually) see:
Able
Baker
Charles
Dominic
Edwards
If you wonder what the line is about: this is a partnership; the names above the line are the people who own the company; those below are employees.
How to get your name above the line?
Work hard and make lots of money/recognition for the firm - you may be offered the opportunity to “buy in” - cut a check for x% of the company’s worth, payable to the company and the partnership agreement will be amended to include you as a partner.
This level of ownership and liability is probably the most distinct definition of “professional”.