'Druim' is the Gaelic for 'ridge', and it often crops up as 'Drum' in place names.
'Greens' is a bit more difficult. It might be from Gaelic 'grian' meaning 'sun', or 'graine' meaning 'sand'. Or it might just be English 'green' as in the colour of grass.
Looks as if Greens of Burgie was not recorded when the Ordnance Survey drew up the Name Books in the mid-19th century so perhaps it had disappeared or been renamed.
Google is useless for finding small places like a single croft or house or a couple of cottages, especially those that do not exist any more. See
https://www.rootschat.com/forum/index.php?topic=758930.0PS The Murray mentioned in the listing in Scotland's Places is 'Mr Murray, Banker'. When the OS were drawing up the Name Books, they asked prominent local people, like the landowners, minister, schoolmaster and so on, how places in the locality were pronounced, spelled and written. 'Mr Murray' was almost certainly Peter Murray in the town of Portsoy, who is in the 1861 census aged 49, born in the parish of Fordyce. Looks as if he may have died in Portsoy in 1886, mother's maiden surname Brodie.