Obsidian (pronounced ob-SID-ee-an) is a black, transparent stone that forms from volcanic lava. Obsidian has been around since the stone age. It was commonly used in the past to make blades and arrowheads, or was polished to be used as a mirror. It has been found across the world - even on Easter island as the pupils of the eyes of their Moai statues! Today you are more likely to find it used as a surgical blade (as it is sharper than steel) and used in jewellery and ornamental objects.
As a name, Obsidian is much rarer than the stone. It seems that it has largely been viewed as a "goth" name because it is seen as darkly exotic. It is also a pagan name, as it is also known as the Wizard's Stone, and is believed to have healing powers (pain relief and lifting depression) and magical uses (protection against negativity and protection when travelling).
A DC Comics superhero is perhaps the most notable Obsidian in popular culture. Todd Rice by day, Obsidian and his twin sister Jade (aka Jennie-Lyn) were founding members of superhero team Infinity Inc. He later worked for the Justice League, before succumbing to a mental illness that turned him into an evil villain. When defeated by the Justice League that he turned on, he overcame his mental illness and returns to the side of good in his retirement years.
Because Obsidian is a rare name people have very few preconceived notions as to whether it is a "boys" name or "girls" name. This is great if you are looking for a gemstone name to bestow on a boy (besides the currently popular Jasper), as most of the commonly used ones have firmly become entrenched in our minds as girls names. I have also recently seen the name Obsydia considered as a fantasy name in a forum on Nameberry, which I think could be a very beautiful variation for a girl. Plus, names starting with "O" are very in vogue at the moment, as witnessed by the popularity of names such as Olivia and Oscar.
If you like your names dark, mysterious, exotic and extremely rare, Obsidian is a definite contender. This is truly a name that your child (or character if you are a writer) could make their own.