All names you,e wrote as examples are actually not Russian. They come from the Bible. So we can find an analogy in all European cultures. Those names are Greece and Jewish and were transformed into Russian.
Екатери́на is the same as Catherine
Елизавета is the same as Elisabeth
Александр is the same as Alexander
Алексей is the same as Alexis
Native Russian names are
Святослав (Sviatoslav). Its diminutive is "Слава" (Slava)
Надежда (Nadezhda). Its diminutive is "Надя (Nadia)
Любовь (Lyubov). Its diminutive is "Люба" (Lyuba)
Владислав (Vladislav). Its diminutive is "Влад" (Vlad)
As you can see the root of the word is present in diminutive form.
Teenagers, boys and girls often use nicknames formed from the full name. In this case, we often have something weird. For example, Екатерина – Катюха (Katyuha)
Russian language has number of inflexional endings. We can transform the name to express the mood. The name Владимир (Vladimir) can be transformed into Вова (Vova), Вовка (Vovka), Вован (Vovan), Володя (Volodya), Вовочка (Vovochka), Володичка (Volodichka), Володька (Volod'ka). Great! Isn't it?