Where it is in our family:
Some say it is a local mispronounciation of Duggan. Others, that its a name in its own right.
The name shows up in the Donegal area, and as she was from the same area as Pat, she way have been of the Ulster families such as the Coyle’s.
Burkes East Galway (a website) sites it being potentially a pre Celtic name, though does say there are other Doogans that are not the same family as the East Galway family.