His name is common to those of the Vikings (of Scandinavian origin), his title in particular to the berserkers, Norse warriors who are recorded in Old Norse literature to have fought in a nearly uncontrollable, trance-like fury, a characteristic which later gave rise to the English word "berserk". Most berserkers wore little to no protection, save a bear skin called a "Bear-sark", which is where the word originated from. The berserkers believed that by wearing the bear's skin, they were able call upon the bear's ferocious rage and strength in battle.
Note that real Vikings did not have horns in their helms, that is just a modern depiction.
In the movie Clerks, the character Silent Bob has a cousin in a heavy metal band that goes by the stage name "Olaf the Berserker".
Olaf's /dance is a direct reference to the Technoviking meme.
Ragnarok is a reference to a string of events in Norse Mythology that heralds the end the gods of era. This was also the beginning of the Man's era.
The Chinese & Japanese character displayed on the icon is 力 (li - chikara), which means "power" in Chinese and Japanese respectively.
Ragnarok crowd-control removement effects is a reference to Poetic Edda strings: "For the forth I know, if men place bonds on my limbs, I so sing that I can walk; the fetter starts from my feet, and the manacle from my hands." That looks like it shouldn't remove silence and blindness effects, like it used to be with old Olaf's ultimate.
Olaf's quote "Urge to kill, rising!" is a reference to one of Homer Simpson's famous lines, from the Treehouse of Horror V episode.
Brolaf's quote, "Bromacia!" is a reference to Demacians and their tendency to shout "Demacia."
Brolaf's taunt "I came here to kick butt and drink Graggy! Looks like I'm all out of Graggy" is a reference to a quote in the 1988 film They Live - "I have come here to chew bubblegum and kick ass...and I'm all out of bubblegum."
Brolaf's other taunt "You can't arrest me, my dad owns a dealership!" is a reference to Aqua Teen Hunger Force, in which two alien bros crash land on earth, and one is constantly telling others about how his dad owns this dealership.
Brolaf's quote "Hey dude, I'm kind of a big deal" may be a reference to Ron Burgundy's quote in the movie Anchorman.
Brolaf's quote "Beatdown City, population - you" is a reference to Deadpool's popular quote "Welcome to loser land, population, YOU!"