From: Chester-le-Street Chronicle and District Advertiser - Friday 14 November 1930
The dish does not, usually, contain plums, the name probably derives from an old usage of 'plum' to mean 'swelled up', as in 'plump' and 'plumped'. George Bell's 'Notes and queries' of 1849 has; "There is also a verb to plum... Dough, when rising under the influence of heat and fermentation, is said to be plumming well." The 'duff' bit is just an old pronunciation of 'dough'.
RH Dana's 'Two Years before Mast' of 1840 has; "This day was Christmas. The only change was that we had a ‘plum duff’ for dinner."
'We scorn digestive pills;
Give us the food that fills;
Who bravely stuff
Themselves with Duff,
May laugh at Doctor's bills.
- from 'The Puddin'-Owners' Evensong' by Norman Lindsay
Plum Duff has a certain association with sailors, though the name may not necessarily have arisen as explained in this article from 1893...
Shields Daily Gazette - Saturday 14 January 1893