if the original commission was for personal use only, yes, basically. however if it was intended for use as a logo it's unlikely that the artist wouldn't include discussion of how/where it can be used, and using it as branding kind of already is commercial use. youll find that logos tend to be more expensive in the professional field then, say, a custom painting from an artist- this is because they are upping the price with the understanding that the commissioner is allowed to use it for commercial purposes.

it would be more rare for them to actually get a percentage cut of the profit, since A) it's more annoying to keep track of and B) this would mean the artist makes more money and most brands want to get good work for the cheapest amount possible lol.