In the Russian language, most first names have diminutive forms that are used to express affection, closeness, or intimacy. Diminutives can also convey status and respect; a young person is less likely to call an elder by a diminutive of the elder's name. Sometimes diminutives are shorter than the full name, but not always. Many names in Russian have multiple diminutives.
The characters in Productivity Zero all have Russian names, and some use diminutive forms when talking to each other:
Dmitri (diminutive is Mitya)
Ivan (diminutive is Vanya)
Mikhail (diminutive is Misha)
Dmitri feels he lords over his household; therefore he will rarely call the bird by his full name Ivan, and use Vanya instead.
Misha, the mouse, wants to establish a bond with Dmitri quickly, so he starts using the diminutive Mitya right away. (I wouldn't recommend this when you first meet someone who speaks Russian).
Ivan, the bird, tends speaks more formally overall, and is less likely to use a diminutive form of a name.