I'd be worried that these names are so out there that you're saddling your DS with something they will have to deal with for the rest of their lives.
I'd be worried that whenever people see or hear their names (even as adults) there will be a rolling of eyes that won't help them. That kind of summary judgment is wrong I know but does happen.
Also the story of Icarus is far too negative for me to saddle a child with that name. You refer to children being called Jack, but the difference is that Jack is a well used name and so doesn't immediately bring to mind Jack the Ripper. Icarus on the other hand is a barely used name so when people hear it they are blind to recall the legend.
Names that are difference are fine, but the overly negative connotations here mean it would be a definite no for me.