I could understand the name John A. Doe, as first, middle and last name. But in some ocassions a name is written as R. Paul Frank. Does that mean R. is his first name in his native language and John is his adopted name in English language?

Some people just don't like their given name and choose to abbreviate it instead.

Some people are actually just given an initial in lieu of a name for either the first, middle or even both.

My uncle's first and middle names were both initials standing for nothing.

I've known people who do this -- my mother and cousin are among them -- because they share a first, but not a middle, name with someone else in their families. To avoid confusion, they've always been called by their middle names. In adulthood, they decide to use only the initial of the first name on official/professional documents, so that people won't actually address them by it.

In some Jewish families, the first name is the Jewish name, and the middle name is the one used as the given name in Europe and the US. Thus my cousin uses what is technically her middle name on legal documents, and very rarely is called by her Jewish name.