I do like the basic concept that you have here. I like the font used for the name. I do not like the star but maybe with a bit straighter lines and something diffent in the logo tis could work. I would like to try a darker (forest) green or some other green color.
fleur de lis has long been regarded as a symbol of strength, power and at the same time kindness. The logo element contains the initials H and C (horizontal)