I googled 'Spud as a nickname' as it was common in my childhood in NZ. My cousin married a 'Spud', (not his real name).
In NZ spud/spuds is also a verncular name for potatoes 'I've got 6 rows of spuds in this year"
Spud as a general nickname for people with Irish surnames names apparently is more common in NZ, as is the use as a name for the potato.
Irish Connection:
Historically, "Spud" has also been a nickname for an Irishman, perhaps connected to the potato's importance in Irish culture and history.
Spud as a specific nickname for people with Murphy is related to a type of potato called a Murphy
In the military context IN WW2 common nicknames in Aus/NZ troops abounded eg 'Dusty' Miller, 'Blue' (for a person with red hair). Usually to celebrate the lack of class levels.