Is there a valid math term? I could just name this guy "sumXY", but that is (a) lame, and (b) not scalable, since going up a dimension would require a rename.
While typing I thought of "componentSum", but I'd love to know if there's a real name for it.
Why not just name it vectorSum where vector is the name of the vector.
If you're taking the sum of the absolute values, it's called the L1 norm (short for Lebesgue 1 norm).
If you're not taking absolute values, I'd suggest just calling it sum, or perhaps vector sum (as others have suggested).
EDIT:
After reading various comments, I'd suggest using the term "element sum". If your vector can contain negative values and you're not taking the absolute value of the elements before summing, it's wrong to use terms like "distance", "length", or "norm". All of those imply one is taking the absolute value of each element before summing.
If your vector is really a vector in the physical sense, there's pretty much no valid reason you would have to add up the components. So I suspect that what you're working with is really a list of numbers (i.e. a CS vector) rather than a true (physics) vector, and you shouldn't worry too much about the naming. 'componentSum' or 'cSum' or 'sigma' even... whatever makes sense to you.