It really depends on where. Some places you'll have no trouble and others you will. Whether or not you'll have problems depends on what you want to do.
I've have the opposite problem in Japan. Virtually everywhere insists that I use the name on my (Canadian) passport as my official name. It's listed as "Lastname Middlename Firstname". Some government offices can handle 3 names (Yay). Some government offices understand the order for Canadian names and since they often can only handle 2 names, will record my name as "Lastname Firstname" (in Japan, family name comes first). Other offices don't understand the order and assume that my single given name has a space in it. Since they can't handle spaces in their software they list my name as "Lastname Middlename". No amount of explanation will detract them as they have to do it the way they've been told.
So now I've got 3 official versions of my name in Japanese official databases (4 if you count the version that is truncated because my name has too many characters). Luckily none of their systems talk to each other ;-) -- though I had one heck of a time getting my "My Number" (similar to social security number) registered because of the confusion. I feel sorry for any Portuguese people (who often have a lot of names) who live in Japan ;-)
The situation in the US is not nearly so bad, but I've definitely heard of problems before.