Those transferring in, as beyphy noted, need to choose a major because they only have two years of study left in their undergraduate careers, and there are higher gpa reqs for a lot of majors, which are all chosen when one is applying, along with possible alternate majors. As a student entering from high school, you have just about an unlimited amount of majors from which you can choose. One of the exceptions would be engineering, which you would have to declare at the time your applying (along with some arts programs similarly).
With this said, there are majors that have higher standards of entry than others, and are generally applied to after two years for students as yourself: Business Economics, Film, Comm Studies. So if you wanted to major in Bus-Econ, you generally wouldn't be admitted to it as a frosh. There are some exceptions, I believe, because I've apparently seen some persons admitted as frosh to the major, generally athletes, eg, a water-polo player, probably because the U is trying to entice them to choose UCLA.
Both majors you specified, as per above, have tough grade requirements for entry. The Business Economics major seems to have prereqs that are more in line with the major and comprise a decent no. of courses, and the Comm Studies seems to have a wider array of interdisciplinary coursework in addition to the two or so intro CS courses (not to be confused with the computer science major). I'm sure doubling in both is doable, but they are in completely different disciplines. The pathway to B-E seems to be more rigid; the pathway to CS seems to be more open within the social-science, humanities depts, but I'm sure you can take the reqs for both within your pre-studies. I know CS used to have a pre-major, which B-E still has, so you can probaly declare pre-econ-biz and do the the CS prereqs, which aren't as set in stone.
With this said, I wouldn't worry about it as much right now; I'd more worry about getting into UCLA, but if you are, go ahead and address these same things on the UCLA message board.