We have three options:
a. (The city name is "White Sands.")
b. (The city name is "White Sands".)
c. (The city name is "White Sands").
We can immediately eliminate "B" as an option, because we know that if a period is required within a parenthetical element ending with a phrase in quotations that it must be inside the quotations.
Now we are left with choices "A" and "C."
Either a period is required within the parenthetical element, or it isn't. If it is, than "A" would be the correct answer. If it is not, than there would be no grammatically correct choice, because if it is not required, than there should be no period on the outside of the parenthetical element. This is because a period outside of a parenthetical element in the middle of a sentence would effectively end the sentence at that point. The choice "C" could only be correct if no period was required inside of a parenthetical element and the parenthetical element was placed at the end of a sentence. If a period was not required, than the correct choice would be:
d. (The city name is "White Sands")
Thus, knowing that "B" is not viable, neither "C," that leaves "A" as the only choice, and the correct one at that.
The answer is "A."