In English speaking countries, there is a fairly common practice of giving children three names: a personal name, a middle name, and a surname. The middle name is almost entirely disregarded in common use and official documentation, but people still have them. It's unlikely that any of the staff will find a name of the form "A B C" unusual at all.
Most likely, if any error occurs at all, the university staff handling your application will simply assume that, upon receiving an application with a name taking the form A B C, that A is your personal name, B is your middle name, and C is your family name, and enter your name into their systems as such. It's unlikely to result in any difficulties in applying, but it might result in them only entering the first letter of B into their systems under "middle initial" or omitting it altogether.
If this occurs, once you've enrolled, I imagine that you would likely be able to just show up at their student administration office and get them to change the name stored in their systems. Students change their names all the time; women in English-speaking names often change their family names when they get married, and transgender individuals often change their personal names when they come out and start transitioning. As a result, it should be a fairly straight-forward process for them to correct any mistakes recording your name in their systems.