What actually forms the brand is the accumulation of everything a customer experiences. How quickly you replied. Whether the price matched the quote. What happened when something went wrong. How the work looked when it was finished. Whether the person who arrived was the person who sold it. Those experiences are what somebody recalls when your name comes up, and no amount of visual design substitutes for them.
The logo does have a job worth taking seriously, and the job is recognition rather than persuasion. It has to be distinctive enough to identify you, legible at the size it will actually appear, and workable in one colour on a background you did not choose. A logo that fails those is a practical problem. A logo that is merely plain is not, provided it is used consistently, because consistency is what converts a mark into recognition over time.
The reason this distinction matters commercially is where the effort goes. A business spending three months and a large share of its budget on identity before it has spoken to a customer has invested in the least determinative element while the determinative ones remain undecided. Who you serve, what you charge, what you promise, and how you behave when it goes wrong are the brand, and they are free to decide and expensive to change later.
There is a practical consequence for the first year specifically. Your positioning will move as you learn who actually buys from you, and a brand built around an early guess frequently needs redoing. A restrained identity survives that adjustment. A heavily thematic one, built around a specific idea of who you serve, does not.
The reasonable sequence is to make the logo good enough and unambiguous, spend the saved attention on being consistently clear about what you do and reliably good at doing it, and revisit the visual identity in year two when you know things you do not know yet. Businesses that do it in that order end up with better brands and usually with better logos as well, because by then the brief is based on something real.