Hi Forfarian
Firstly I haven't heard of Edward Picton Baumgarten. I looked on FindMyPast to see if there was marriage certificate that may have given a lead into his parents. There is no actual certificate and only a transcription which incidentally gives the location of marriage as HONITON, Devon.
In relation to the names there could be a number of reasons. Confusion around names was an issue for me when I first started researching the line of Picton Warlow and the related lines of Craven and Picton Tubervill etc. I have found that the usual reason seems to be one related to inheritance.
Case in point and in this instance there were 2 changes of name as follows.
10 Feb 1842 - Goodwin Charles Colquitt assumed the name of Goodwin Charles Goodwin. Then "Whitehall, December 12, I860.
The Queen has been pleased to grant unto Goodwin-Charles Goodwin, of Brockhampton Park, in the parish Sevenhampton, in the county of Gloucester, Esquire, in the Commission of the Peace for the said county, late a Captain in the 5th Regiment of Dragoon Guards, and Georgina Maria, his wife, only daughter of Fulwar Craven, late of Brockhampton Park aforesaid, Esquire deceased, Her Royal license and authority, that they may (in compliance with a proviso contained in the last will and testament of the said Fulwar Craven), henceforth assume and take the surname of Craven only, and that the said Goodwin Charles Goodwin, may bear the arms of Craven and that the said surname and arms of Craven may in the like manner be taken, borne, and used by the issue of their said marriage such arms being first duly exemplified according to the laws of arms, and recorded in the Herald's Office otherwise, the said Royal license and permission to be void and of none effect: And also to command that the said Royal concession and declaration be registered in Her Majesty's College of Arms."
This may be a reason why the changed names - perhaps check the Gazette? No matter what it creates a challenge as people have then assumed the double barrel names and I am no expert on it at all.
Mocavo have a bit of information on him
http://tinyurl.com/mfqo5xzI then checked out Welsh Newspapers Online and came across some articles related to Edward
http://tinyurl.com/luqm272 - this relates to his treatment by his fellow officers not in Australia but in Canterbury
http://tinyurl.com/qygozru - same topic but different article
http://tinyurl.com/lwwro8u - different topic but one in which both name variations mentioned
Nonetheless when I have been stumped I have posted my question to RootsChat Forum and with the wonderful Chatters, a number of seemingly brickwalls have come tumbling down. Today was one of those.
I am sorry I couldn't be of more help. Attached also is a snippet I located which may be of some small assistance.
Westy11