If it makes you feel any better, my most recent and my most favorite barbarian I've ever created is a minotaur named Bongus and whenever he enters rage, it's because he's deathly scared of whatever we're fighting, and get's so scared that his Fight-or-Flight response kicks in, and, being slow, it's really only ever Fight.

I always imagined rages as adrenaline or even hysterical strength.

I have the idea for a Barbarian that is actually a regular guy with a demon inside his soul. When he rages its actually the demon taking control. The demon obviously has a bloodlust so, of course, death ensues. I haven't played him yet but that's kinda what I thought of when I read this.

You can have a barbarian whose personality isn’t their rage. Only one barbarian subclass is the berserker.

I have a Barb that is a Path of the Ancestrial Spirit, that suffers from a form of PTSD after her family and clan got murdered from a set up mission they took on.  Her deal is she really only rages when an ally gets injured(yes a little counter intuitive of the subclass but, eh character flavor)  as she remembers the pain she felt from losing her family.  I usually describe it as not really a rage but more that her mind goes into a defensive blank as her body kind of does its own thing to protect her fellow allies. 

My DM does a kind of kool thing where she would hear the whispers of her family saying things like "No, not them to?" Stuff to that extent.  Very fun to play.

My Half-orc barbarian (named holth) is usually very emotional, for all the emotions. He weeps at the falling of his friends, cheers at the vanquished of his foes, yells during combat. However, during the rage, all emotion goes away. He locks in, runs his finger along his jaw, and shows his foes the very definition of a perfect warrior, and jaw.

I like "angry hit people" mode. My Half-Orc Barbarian (Berserker), Lilorish, is always quick to confuse/quick to anger, so it naturally goes with her in battle. She gets bored easily, and tires of talk about plans and whatnot. She still tries to follow when her party makes a plan because she doesn't want to ruin it, understanding that the plans are important to those she cares about, but she just doesn't like to sit there and listen to them making the plan cause it bores her. For her, the Rage isn't exactly like she just gets angry, it's more primal I think for her. Like she doesn't often care about social norms, anyway, but when she rages she sorta lets go of all social conventions and just becomes one with raw, primal fighting. The fighting and the blood makes her feel alive, she loves fighting. So I guess her rage is less "angry" and more just getting in tune with her fighting spirit. That includes yelling, laughing and looking "angry".

Whereas my Dhampir Barbarian (Beast), Reynvia, she is kind of frequently annoyed, finding several of her partymates annoying as all hell and only joining them because her dear friend requested her to and they are trying to find him, so she feels required to stay saddled with these annoying folks. She doesn't care about them, though, and is quite selfish. Her version of raging is less angry, just getting mad and whacking things, but similar to Lilorish she connects to her fighting spirit and instead of getting loud and boisterous, she becomes more sadistic looking, silent fighter, enjoying the blood and viscera around her, licking the blood from her body as she gets splashed in the fight and staring her enemies down with a smirk and a cold expression. She becomes primal, as well, but it is presented in a different way than being outwardly filled with emotion.

Lilorish is a lot closer to the "angry hit people" rage, but that's not how I mentally imagine it, being so one-noted. There's a bit of nuance in how I like to envision it, although I may not describe it well, I think I at least do a decent job of roleplaying it well?? She's an emotional character overall, so it makes sense that her rage would be, well, rage-filled.

My Barbarian just loves everyone, that’s all.

https://m.youtube.com/watch?v=pxvzEfI0BFU

My barbarian is full of love.   
https://m.youtube.com/watch?v=X94AdCNKAQY

For my character, it was this sort of drunk on power ego trip, when he rages, he sees himself as this unkillable war machine, barreling through enemies. 

Yeah, me too. I tend to make my barbarians actually have a nature side to them. It contrasts the primative state that they only have. In fact one of my favorite characters was a barbarian with one level in druid to contrast the main class.