#5 is amazingly similar to the logo I've been using, only much livelier with the addition of colour. I wonder if you could somehow get a sense of motion in there somehow? Also what would happen if you dropped the Ltd and just used the word Designs under Zizi. Having the dragonfly's body touch the dot of the blue i bothers me a little. Creates some visual confusion. Could you also try a B/W version of this one?
Not quite sure why I like #6 less. I think it has to do with the smaller size of the dragonfly next to the bolder black text. Otherwise, similar comments as for 5.