Parents of James Pinkerton (1819 - 1904)

James Pinkerton, [Free 1861-1863]
the record for James Pinkerton presently shows his parents to be James Pinkerton & Martha Moore, however the information provided by NSW BDM Death records indicates his parents as James & Matilda.
I don't believe 'Martha' is a diminutive for 'Matilda'
Anyone have any further information on this?

I note that most public trees show 'Martha'