The family name of "White" could have several deeper meanings. For example, the central conflict of the story is a cursed object -- the titular Monkey's Paw -- that was imbued with magic in India. For the stolid, simple upper-middle-class family of the Whites, the foreign land of India represented something strange and mysterious; their name, representative of their skin color, could refer to their utter inability to recognize the danger of the Monkey's Paw and even to a race-based superiority complex.
"I'd like to go to India myself," said the old man, "just to look round a bit, you know."
"I should like to see those old temples and fakirs and jugglers..."
(Jacobs, "The Monkey's Paw," gaslight.mtroyal.ca)
Because they cannot understand the culture and history of India, the Whites are prevented from keeping their lives safe and comfortable. They believe their Western culture is superior and so they cannot be in any danger; their "whiteness" blinds them to the idea that a different culture, with different beliefs (and, of course, magical abilities) could affect their lives.