While I can't fully answer the actions of Ivan IV, the Terrible, I will offer a brief note about the name itself, and why it is a modern misnomer. In Russian he is known as "Иван Грозный" or "Ivan Grozny" in its transliterated form. Grozny is commonly translated now as "fearsome" or "formidable"^1 However the word "terrible" was used in a similar context in older English, so even though the word itself has changed, the sobriquet of Ivan IV in English has remained the same, leading to modern perceptions that he was unusually cruel.

1. Note that the capital of Chechnya has the same name; it was established as one of a series of forts in the northern Caucasus during the Russian conquest there, with others taking similar names. One I can think of is Vladikavkaz, which means "ruler of the Caucasus".