I just saw this video explaining some cultures don't even have a separate word for hand. The reason- because they don't need it. If you don't have articles of clothes or any reason to make something distinct there won't be a word for it. I imagine, the reason thumb has a seperate word is probably because of gloves. You need a way to describe the funny finger to be able to make something for it. Not 100% sure though.

Calling it the big finger would not be accurate either. That would imply its bigger than the middle finger in both length and width.

Proto-Indo-European root: “Tum” means “to swell”, which describes the thumb’s shape.

The video: