Since the OP was open to any commercially available offering...
The "IBM InfoSphere Global Name Analytics" appears to be a commercial solution satisfying the original request for the parsing of a [free-form unstructured] personal name [full name]; apparently with a degree of certainty in regards to resolving some of the name ambiguity issues alluded to in other responses.
Note: I have no personal experience nor association with the product, I had merely encountered this discussion and the following reference links while re-investigating effectively the same concern as described by the OP. HTH.
A general product documentation link:
http://publib.boulder.ibm.com/infocenter/gnrgna/v4r1m0/topic/com.ibm.gnr.gna.ic.doc/topics/gnr_gna_con_gnaoverview.html
Refer to the "Parsing names using NameParser" at
http://publib.boulder.ibm.com/infocenter/gnrgna/v4r1m0/topic/com.ibm.gnr.gna.ic.doc/topics/gnr_np_con_parsingnamesusingnameparser.html
The NameParser is a component API for the product per
http://publib.boulder.ibm.com/infocenter/gnrgna/v4r1m0/topic/com.ibm.gnr.gna.ic.doc/topics/gnr_gnm_con_logicalarchitecturecapis.html
Refer to the "Parsing names using IBM NameWorks" at
http://publib.boulder.ibm.com/infocenter/gnrgna/v4r1m0/topic/com.ibm.gnr.gna.ic.doc/topics/gnr_gnm_con_parsingnamesusingnameworks.html
"IBM NameWorks combines the individual IBM InfoSphere Global Name Recognition components into a single, unified, easy-to-use application programming interface (API), and also extends this functionality to Java applications and as a Web service"
http://publib.boulder.ibm.com/infocenter/gnrgna/v4r1m0/topic/com.ibm.gnr.gna.ic.doc/topics/gnr_gnm_con_logicalarchitecturenwapis.html
To clarify why I think this answers the question, ameliorating some of the previous alluded difficulties in accomplishing the task... If I understood correctly what I read, the APIs use the "NameHunter Server" to search the "IBM InfoSphere Global Name Data Archive (NDA)" which is described as "a collection of nearly one billion names from around the world, along with gender and country of association for each name. This large repository of name information powers the algorithms and rules that IBM InfoSphere Global Name Recognition products use to categorize, classify, parse, genderize , and match names."
FWiW I also ran across a "Name Parser" which uses a database of ~140K names as noted at:
http://www.melissadata.com/dqt/websmart-web-services.htm