The script styled "F" is all wrong with the uppercase letters in the rest of the company name.
The uppercase "L" in the word "Low" doesn't fit either. You really should avoid mixing and matching font styles in the same word. It'd read much better were it the same font style as the rest of the bottom line.
Better to use the same font face for the entire top line or try it with just the word "Flowers".
This one's a natural for a stylized graphic involving a flower of some kind. Perhaps a flower made of or lit by spotlights. Lots of bright primary colors to catch the eye.
Give potential clients something to remember. Make "Flowers" the focal point of the graphic.
Quite honestly, you'll be miles ahead in terms of "brand name recogition" if you hire a graphic designer, who specializes in logos, to do this for you.
The colors might be all wrong and the font face may not grab you, but here's a concept image for you to consider. Think about shaping the elements that comprise the flower and the general outer shape in your new logo as spotlights. You might even consider Keeping the word "FLOWER" partially outside the "guitar pick" shape.
Good Luck.
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