Although I really like your website -- simple, to the point, showcasing your work well -- I feel that the logo is a little too trendy and similar to several other logos. The container especially makes it less unique than it can be. The Bahamas identity [link] was, IMO, the first to use this effectively and it's been heavily overdone ever since. Maybe you could consider having the symbol without that container?
The shape inside is relatively more unique and memorable and serves the purpose better. The entwined-double-d design works well for the name.
Personally I prefer the symbol inside the shape, the fact that it's been heavily overdone, I totally agree with you, although I didnt saw an example and got the feeling "I have to do something like this, but just by playing around with circles and the shape I got this. This also reminds me an story of an teacher, with an advertising company that was using an very overused stockphoto and he called them arguing why they were advertising with an image that was clearly not made by themselfs, after a couple of seconds they replied "sure... and now you may guess how many percent of my clients knows that"
Ultimately it's your design man. My point is not whether your clients know about all the other logos and identities, but whether you would like to do something more creative for your own satisfaction as a designer. Otherwise it's just another business tool, not a passionate design. Anyway good job on it.
Very nice logo indeed great flow and shapes .................................................. but I hate the use of the red as a hover state on your new website, it's just too bold imo, cheapens the look, I would go a darker grey instead