Do entrepreneurs and business owners need to worry about their personal brand?
Whether you are working on your personal brand or not, then that's your personal brand itself. If I can't find anything about you, perhaps only an empty LinkedIn profile -- that to me is your personal brand. It just means that you don't really do much or it doesn't look like you do much in that social media channel.
If I'm going to make any kind of purchasing decisions, then I may go with someone who's put more effort in their personal brand simply because they are encouraging me to know, like, and trust them.
An entrepreneur or the owner of the business needs a personal brand for various reasons, but ultimately it is to let people know more about you and what you stand for, then get to like you and delve deeper into seeing what you do, who you helped, and how you helped them. If I'm interested in you, then I'll get more interested in your company and the more likely that I am to buy or invest or work with you.
It's important not to hide behind the logo of your company but to actually work on your personal brand.