Why are most given names so common?

First names are subject to Zipf's law of distribution (see this paper for some examples). This means that the most frequent name is roughly twice as common as the one after that and so on. The same applies to frequencies of all the relatively frequent words in the corpus of any language.

But it's not clear what causes this type of distribution because it appears in a lot of systems where human intentionality cannot play a role.

With names, it's obvious imitation plays a key role (like fashion) - so not surprisingly the most popular names always happen in clusters over a period of time. (For instance, my first name was incredibly rare in the Czech Republic until the growing fame of the hockey player Dominik Hasek - now, while still not very frequent, it is much more common. In Albania, for instance, you have a relatively lot of people born during a certain period called Lenin.) The sorts of names being imitated will vary a lot across cultures.

You should also keep in mind that there's huge cultural variability of what a 'given' name means. From no special given name (first son, second daughter, etc.) to ones chosen (and changed) to indicate quality or some events (Sitting Bull). As far as I know, no frequency studies have been done on these non-Western style naming systems.

The current US African American preference for novel names referencing African patterns would also make an interesting case study. Would a system where the main aim is to be different still be subject to Zipf's law?