Actually, "little falcon" is a literal translation of the Russian word sokolik, an intimacy or endearment that is still used by older people. The Russian language is full of such words: First, the Russian national character is expressive and emotional, and one aspect of it is that it has so many diminutive adjectives and nouns (hence attempts to render them in English by the word "little"); second, the language itself offers a variety of ways to be expressive and emotional. One of them is suffixes. Russian is sometimes called the language of suffixes.
Russian suffixes express an extremely wide range of emotions and attitudes. They can produce words that are caressing, diminutive, familiar, vulgar or contemptuous.
Polish linguist Anna Wierzbicka studied the way Russian suffixes work with Russian personal names. She says the meanings expressed by names with suffixes are so rich and complex they cannot be represented by simple labels such as "affectionate" or "scornful". Some are ambivalent. The suffix ka (as in Mashka) may express familiarity or "anti-respect" but it becomes diminutive and even caressing in Mashenka.
Ik (the suffix used in Karataev's sokolik) is diminutive when used with masculine names. People use it when they talk to small boys, who begin to resent it in their early teenage years.
In English, suffixes are rarer, and they are less expressive. Most commonly, standard short forms such as Tom or Bill are used with regard to people one knows well. Sometimes, such short forms are preferred by the person and are used officially as in Jimmy Carter rather than James Earl Carter, as Leonid Brezhnev's letter of congratulations was addressed to the then president-elect.
Translators of fiction face enormous problems rendering the expressive range conveyed by Russian suffixes. I've noticed recently that simple shortening has become widespread, at least in male names. Increasingly, people prefer to be called Vlad or Stas. We'll see how that plays out.