What's this logo look like?
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IMO, it would be better to have a single object as a logo, else the two will fight for space.
Have you considered the idea that the bee's wings looks like the letter 'B'? A lowercase cursive 'b' could be tweaked to look like a cute bee.
I agree with the idea to include your name with the logo. McDonald's, Apple and Adobe used to have both name and icon on packaging until they figured their brand was popular enought to be just icon.
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Taking time to think about it, I think I'm in the "single object" camp as well. If I were to recommend to a company what to do from a branding perspective, it would be to make the icon just the Bee in the circle and remove the "B", then create variations that included the bee circle icon by itself plus versions with it paired with the name.
I really like the way the bee is drawn so I think it would stand out in a distinctive way on it's own.
At the end of the day, the connection between your name and the bee will be vague until someone meets you or reads about you on your website. So the job of the brand is to be immediately distinctive and unique, and then to reinforce your personality even after someone gets the symbolic connection.
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I saw the number 3, before a B, just at first fast glance.
The bee looked like a pendant to me, with the antennae being the chain, but I deal with jewelry a lot, so my brain is wired to see that I guess.
The eyes are the same size as the wings, at first when I looked at it closer I saw a really cartoony fly. I dunno, just thoughts.
I would draw a few bees, see if any of them feel right. Can always stick with the original.
