This is a nice effort though there several issues with it. Please not the following is offered only as constructive criticism. Do not take anything personally. Please note that I went to college for art and design and worked as a graphics designer for a few years before becoming a programmer.
First thing this is technically not a logo. A logo is a distinguishable graphic. A logo should be able to be used on a business card or letter head, where it is printed much smaller, and still be recognizable. As well a good logo should also be able to be printed in high contrast, (just black and white no grays). Examples of this would be the Nike Swoosh, the Disney mouse ears, the Olympics rings, or Apple's apple.

Those are all purely graphical elements with out type that immediately indicate the company or organization they represent. That is a logo. The image you have is closer to being a logotype. (pulled the image from this
nice explanation of types of logos)
Now that that is cleared up there is something else we need to know. The purpose of a logo is to distinguish a company and to identify a company. A companies logo or logotype should say something about it indirectly. Two ways of doing this are with type and color. to use the IBM logo as an example you will see that is is just the name of the company (breaking the the type rule) but, the line through it bespeak technology, especially to those a bit older who are used tp to print outs from dot matrix printers and older monitor displays. The logo is, when in color, in blue. Blues are typically used used to denote stability and respect in design. Similarly when type is is used it needs to be either unique, like the NASA logo or be representative of the organization. For example you should probably avoid an accountant who uses comic sans on his business card.

Concerning your logo directly; Let us remove all but the actual company name and reflection. The font (the name of which escapes me) is completely wrong for the type of service AstaHost provides. I would expect this typeface for a web comic or something of that sort. It is too "fun" for a service where stability is preferred. Also the type is rather plain, I have seen the type many times. Consider looking around the internet for a more unique type, (falsely called a font), consider adjusting the kerning (the space between individual letters) as this can make a type more interesting to look at. The reflection bit is overused in my opinion in too many logos.
This response has been MUCH longer than I had anticipated, thus I will end it here. Take a look at the above link for a nice example of some logos. If you are interested in design take a look at
Designing with Type. Or any other number of good design books. A warning though most "design" sources on the net are absolute crap.